Nancy and Metz and two relatively large cities, close to each other along a North-South axis. They are not big enough to support two distinct airports, two high-speed train lines (which necessarily run East-West since they come from Paris…), etc. Consequently, many infrastructure projects are built half-way between the cities, which is not really satisfying for either of them (the one exception is the A4 motorway, which drives through Metz, far away from Nancy).

Nancy-Essey is not really a commercial airport anymore. It never was very big and all scheduled flights stopped when Metz-Nancy-Lorraine was put into service. Metz-Nancy-Lorraine is one of these infrastructure projects in the middle of nowhere and is not even connected to the train network (even though both the North-South line between Luxembourg and Nancy and the high-speed line between Paris and Strasbourg are not very far). Also, since the “LGV Est” (East high-speed line) was built, Nancy or Metz are only one and a half hour from Paris by train, which killed all demand for flights to Paris so there are none.

The high-speed train line between Paris and Strasbourg faced the same problem. Trains to Strasbourg cannot stop or run through both Nancy and Metz, they have to go through one of them or in the middle. The final choice was to build the line in the middle and to build a new train station (called “Lorraine”), which is far from both cities and not even connected to the North-South line. That station receives trains from cities other than Paris (“province-province TGV” as they are called in France) but not from Paris and sees very little traffic, just like the Metz-Nancy airport. Trains from Paris go either to Metz, Strasbourg or Nancy (reducing frequency to each of these cities).

In practice, it means you can't fly to Nancy itself (short of chartering a small business jet) and the train connections are not as attractive as you might hope for. This leaves you with four main options:

• You could conceivably fly to Metz-Nancy-Lorraine from either Lyon, Marseille, Nice or Toulouse (but not Strasbourg, which is really really close) but that would be very inconvenient as you would probably need two layovers in Europe (neither of these airports is a major international hub). And then you would not be in Nancy and would still need to take a bus. If you really want to, you can find such flights (e.g. somewhere-FCO-LYS-ETZ or -AMS-LYS-ETZ), e.g. on ITA Matrix.

• As suggested in another answer, Amsterdam is not that far (in straight line) and it's a major hub so it's easy to reach from the US but the train connections to Nancy are cumbersome. You can either go through Paris, which is actually quick but tends to be expensive (and then why not fly directly to Paris?) or through Belgium, which is painfully slow with several changes. There are no fast direct trains. Technically, FRA is even closer but I think the connections are even worse.

• Luxembourg is a bit better, it's an international airport and it's the closest to Nancy but the public transport connections are not very good. It should be possible to go to Nancy in less than two hours (with either a bus and a train or a private shuttle/taxi). It could still be an option but since there are no intercontinental passenger flights landing there, you would need at least one layover somewhere else in Europe.

• The natural choice is flying into Paris Charles-De-Gaulle. Unfortunately, there are no direct trains from the airport to Nancy itself. It means that the only solutions are (a) going to the center of Paris with RER and then connect to a TGV to Nancy or (b) taking a TGV to the Lorraine train station (the one in the countryside) and then taking a bus to the center of Nancy. That will take about two hours too.

Nancy is a medium-sized town, 1½ hour away from Paris by train. That's too small to sustain flights between Paris and Nancy. The Metz/Nancy airport has infrequent connections to a few other French towns which lack convenient train connections, and to a few international cities that people fly to from Nancy. But Nancy's main airport is Paris.

There are two reasonable ways of traveling between the US and Nancy. Both involve taking a flight to Paris (all flights land at the Roissy CDG airport). Then you have two choices:

• There are a few high-speed trains between the Roissy TGV (high speed train) station and the Lorraine TGV station which is between Nancy and Metz. The TGV station is right below terminal 2 and a free bus or train ride away from terminal 1. At the Lorraine station, a connecting bus takes you to Nancy. The trip time is about 2 hours.
• There are more frequent trains between Paris Est and Nancy (and a few more between Paris Est and Lorraine with a connecting bus). To reach Paris Est from the airport, take RER B (suburban line) to Gare du Nord, and either walk or take the metro for 1 stop. The walk is short (5 minutes, a bit more with luggage), but not very well signed. The metro is not necessarily less tiring with luggage because you'll need to go down and up a few flights of stairs. The total trip time is about 2½ hours.

Take a flight to Paris, and book a connecting train from the French railway authority. TGV need to be booked in advance, the sooner the cheaper. If you go via Paris, buy the suburban ticket at the airport station. The German railways website has a more convenient interface to research schedules, but it won't sell you a ticket for a trip outside Germany.

A cheaper option is car sharing — I see 18€ on one site (which I neither recommend nor disrecommend). You probably won't be able to schedule that months in advance though. There is also at least one shuttle (a lot more expensive). I don't think there are any scheduled buses between Nancy and Roissy, only between Nancy and Paris (with Eurolines); that's likely to be cheaper than the train but a lot slower and reaching the Paris Eurolines bus station is not very convenient.

The nearest airport to Nancy that handles commercial traffic is the Metz–Nancy–Lorraine Airport, which is somewhat far from the town of Nancy. According to Wikipedia:

Ground transportation

A shuttle bus to Nancy and Metz meets every departing and arriving flight. The journey takes about 30 minutes and costs 8 euros.

Since this is a smaller airport, flights to this airport probably don't depart from CDG in Paris. Instead, they are more likely to depart from Orly (though I haven't looked it up). This could be why you cannot find connecting flights.

I just looked on FlightAware for LFJL and could not see any scheduled flights to or from Paris.

The trains in France are very good and the Gare de Nancy is right in the centre of town. I am not sure why you would put up with the inconvenience of flying for such a short distance in Europe when the train would probably get you there faster anyway.

There are flights from the USA to Lyon and then from Lyon to Metz/Nancy, but I am not sure which airlines have interline agreements with Airlinair (who apparently are the only carrier to serve Metz from Lyon). You might need to book separate tickets, though you could check both KLM and Air France websites.

You could fly to Amsterdam, Paris or Luxemburg and hop the train. Air France will even sell you a ticket with both your flight from the USA to Paris, plus the train ticket.

In terms of travel time, you likely will find it quicker to use the train, rather than flying south to Lyon, waiting around in the airport, then flying back north to Metz.

Fly to CDG and Take the TGV

Of all the already mentioned solutions, I think the sanest are either the TGV from CDG to Gare Lorraine TGV, followed by another train to Nancy. Or CDG to Gare de l'Est via RER/metro, followed by a TGV to Nancy Gare Thiers (the central station). Since I currently live here I can only say "been there, done that".

Sounds awfully complicated because it is, seeing as there is no direct transport to Nancy (or Metz for that matter since the authorities decided to go full crazy and place both airport and TGV station halfway between the two cities, to supposedly make everyone happy). Another possible downside is the cost since trains, and in particular TGV's, in France tend to be very expensive. Unless one has a discount card for young people (18 - 27y) or for senior travellers, in which case very interesting discounts -- up to 60% -- can be obtained.

Enter: Car-Sharing

I often say this on this website: car-sharing recently became very popular in France. The reason is that there are plenty of car commuters, probably due to the hefty train costs, and often these cars carry only the driver. So people starting asking themselves why not pick-up a fellow traveller to make a few extra bucks? Recently there has also been an increase of people who drive popular routes on purpose making a living with car-sharing services. So the point is: Paris to Nancy by car is realistically 4-5h depending on which road is employed -- paying motorway or national road. And it costs around 20€ one way.

I have plenty of colleagues who rely on such services. Turns out they get to ride into more high-end cars than you would expect. One example of car-sharing website is blablacar.

I support your original idea: Flying to Strasbourg SXB, taking a local train from the airport downtown (costs like €4, can be bought at the station, and takes like 20 minutes), visiting the Strasbourg city centre since it's really beautiful, and then taking a TER train from Strasbourg to Nancy (the ticket costs at most €25, less if you book in advance, it takes 1 hour 20 minutes).

I have done this when my flight to CDG was cancelled and I managed to re-book to Strasbourg (that's why I know the maximum price for Str-Nan train). I certainly don't complain in the end since the visit of Strasbourg was really worth it!