Schengen visa application at French consulate in India. Currently residing in the USA on H1B

It might be possible, but only if the French consulate in India accepts that you have "provided justification for lodging the application at that consulate" (Schengen Visa Code Article 6, paragraph 2).

If you look at the handbook for the processing of visa applications, you will see that the traveler's convenience is not generally sufficient justification. For example:

Example: A Moroccan national who spends his holidays in Montreal (Canada) wishes to apply for a visa to travel to Germany at the German consulate in Montreal. He claims that the waiting time for obtaining an appointment for submitting the application at the German consulate in Rabat (Morocco) is too long.

The German consulate in Montreal should not accept to deal with the application, because the justification is unfounded.

However, if your May trip has been scheduled recently, and your April departure is too soon for you to be able to get a visa before you leave, your justification might be sufficient. For example:

Example: A Russian businessman from Novorossiysk (Russia) has travelled to Moscow (Russia) for a trade fair. There he meets a Greek business person who invites him to come to Athens (Greece) straight away in order to establish a contract for a future business relationship. The Russian businessman wishes to apply for a visa at the Greek consulate in Moscow because the approximate travel/road distance between Moscow and Novorossiysk is around 1400 km.

The Greek consulate in Moscow should deal with the application because it would be excessive to require the person concerned to return to his city of residence to apply for the visa.

On the other hand, if your trip has been planned for a while, then the consulate in India will likely find the justification insufficient, because you could have applied in the US in February or March.