transit visa in Frankfurt on advance parole

It seems you will need an airport transit visa for Germany to transit through the international transit zone.

There is a database called Timatic that practically all airlines use to determine whether a traveller is permitted to apply for entry at their destination country. It is important for airlines to check whether the traveller has to correct type of documents that seem valid as they would otherwise be subject to hefty fines or other punitive measures. (They are not, however, required to perform full checks of validity as an immigration official would. This would be an undue burden.) The database is not always fully up to date but it is very difficult to argue your way through to the plane if Timatic says your documentation is insufficient.

The link above leads to a web form that you can use to enter your own details into Timatic. I obviously had to guess a couple of things. I guessed that your passport will expire around five years from now and that you do not have a return ticket from the US although your trip consisted of only one ticket.

I then ignored the part about the US itself. When I come to the part about Germany, it reads:

Visa required.

Transiting without a visa is possible for:

Nationals of India transiting through Frankfurt (FRA) or Munich (MUC), arriving from a non-Schengen Member State with a confirmed onward ticket for a flight within 24 hours to a third country which is not a Schengen Member State. They must:

• have a visa issued by Bulgaria, Canada, Croatia, Cyprus, Ireland (Rep.), Japan, Romania or USA, and
• stay in the international transit area of the airport, and
• have documents required for their next destination.

As you do not currently hold a valid visa for the US, the airline is likely not going to allow you to board.

Changing your document from an Indian passport to an 'Authorization for Parole of an Alien into the United States' does not change the part for Germany although the problems stateside disappeared from the output.

In the comments you mentioned that the same was true when you were flying from the US through Germany back to India, having only an expired H1-B visa in your passport. However, Timatic gives the following output:

Visa required.

Transiting without a visa is possible for:

[...]

Nationals of India transiting through Frankfurt (FRA) or Munich (MUC), arriving from a non-Schengen Member State with a confirmed onward ticket for a flight within 24 hours to a third country which is not a Schengen Member State. They must:

• have a used, valid or expired visa issued by Bulgaria, Canada, Croatia, Cyprus, Ireland (Rep.), Japan, Romania or USA, and
• be returning from the country that issued the visa, and
• stay in the international transit area of the airport, and
• have documents required for their next destination.

The difference here is that your expired US visa allows you to travel somewhere else if and only if you are returning from the US and have documentation as required for your next destination. The typical case will be somebody on a tourist visa with a layover both outbound and inbound; outbound, they will be able to use their visa as issued by the US, inbound the expired visa will allow them to return home.

Exceptions:

Nationals of above listed countries do NOT require an airport transit visa if

1. they hold a valid visa for the United States of America, or
2. they hold a used valid or expired visa issued by the US, return from the US and travel to a non-Schengen Member State within 24 hours after the visa expired.

The above is from German consulate in USA. The statement that travel should be within 24 hrs of visa expiry make it clear that transit visa is needed after 24 hrs of H1B visa expiry

See Airport Transit in Germany and Airport Transit Country List (PDF), which is the source of the quotation above.