How can I apply for a 2-month tourist visa for Thailand while I’m in India?

You can only apply via the consulate that serves your physical location at the time but if you don't have Indian residence I don't think you can apply from their anyway so your only option may be to return visa exempt

The waiting time for visa approval could be longer than your stay

You apply with your French passport through the Thai Embassy in New Delhi or the consulate in Mumbai, which handles e-Visa applications from all nationalities staying in India.

Just to add, the Thai Embassy in New Delhi states a processing time of approximately 14 working days. With your return flight on 1 December, you’ll have less time than that, so I strongly recommend applying immediately upon arrival in India.

Shouldn't be a problem,

Apply as French because that's your Passport nationality,