French rules for long stay visa: OFII

I'm guessing that when you say you'll enter France with a Long Stay French Visa, you mean you'll have a "visa de long séjour"?

All the details you should need are on the website of the l'Office Francais de l'Immigration et de l'Integration (the OFII), though they're only available in French. The page that should cover your situation is this one, and there's a very detailed Wikipedia.fr page on it too.

Under Schengen rules, a French resident (who isn't also an EU citizen) is allowed to visit other Schengen countries for up to 90 days at a time. The problem is that an un-validated Visa de Long Séjour doesn't seem to qualify you as a resident, that only happens when you go through the OFII to get it validated. Once validated, they'll issue you with a sticker (vignette) which goes in your passport by your visa. If you don't have the vignette, then if you leave France (including to visit another Schengen country) then technically you're not entitled to return until you get a Visa de Retour Consulaire

So, it looks like you're not technically supposed to leave France until such time as you've applied to the OFII for your vignette, you've filled out the appropriate forms and completed the appropriate linguistic tests / medical exams / interviews (as required), and it's been issued by the OFII. Could you get away with it? Maybe, especially if you don't fly, but it's pretty risky as if found you could potentially be deported home from the country you're in (assuming you didn't also get a short term visa for there), and then have to get a Visa de Retour before you can fly back to France...

One thing to be aware of is that the rules changed on the 1st of September 2009, but a lot of the resources you'll find on the internet about the "visa de long séjour" pre-date that, and talk about a residence permit (carte de séjour). You should check with the OFII website / your nearest French embassy to be sure that you're covered by the new rules where you don't need to go down that route (from your question it looks like you don't need it), and then make sure any websites you're reading about the process are new enough to cover you!

I wish I had a source for this, but I was in this exact same situation an year ago. As an Indian Citizen, we do not get visa-free travel to the Schengen Countries.

Thus, me and two of my friends were a special case for the French Consulate in Atlanta. They informed that if we were to travel without the stamp, we could travel up to 5 days outside the country without entering the country before.

Similarly, we could have chosen to do the same up till 5 days after my Study Abroad program was over as well, but only one of the two, not both together.

Thus, we entered the Schengen Area in the Netherlands and the proceeded to take a train to France wherein we stayed in the country country until our OFII stamp was issued.

As @Gagravarr mentions, the visa is only valid for within French travel without the stamp and can be treated as a "Schengen Visa" only after it has been stamped, but you can travel up to 5 days before or after it.

Note: I believe the 5 day rule is relatively recent as the French Consulate informed us and it was possible to travel for a greater number of days before or after the official duration of the program before 2012 or so.

The answer is NO, you need the stamp to do anything in europe. Since you are under a long stay visa and not a schengen it's mandatory