Ah, I was thinking about posting a thread like that just yesterday!
I agree with Matteo, much like China in the late XIXth century, India was the golden goose of the XVII-XVIIIth centuries.
Money isn't the a problem as long as you have India and the means to secure it. Even Asia to Asia commerce would be enough to sustain it, let alone exportations to Europe...
I would say the problem is more political than anything else. The French never knew how to properly dose state intervention in their East India Companies. It went from too much with Richelieu to not enough with Dupleix.
Dupleix pionneered the alliance/protectorate tactic that the Brits would later use with great success. If I recall, he was called back to France because he was TOO successful and the company deemed it too costly.
That's also a tension that was ever lasting in the BEIC but didn't stop them.
I wouldn't exactly know why, I would say that maybe the English high class was more stable, economically and politically? That's pure and absolute speculation on my part, do break this argument in shards if you can.
The French can, and almost did take over India, or at least the Southern half.
From there you have several PoD:
*Dupleix isn't called back and keeps reinforcing the French position
*The French don't give back Madras after the treaty of Aix la Chapelle. Maybe Louisbourg is ransomed against some sugar island or something like that?
*The battle of Plassey is lost by the Brits, helping the allies of the French assert their dominance.
If you wanna be cheeky you can always try something a bit different:
Just before the Revolution, an expedition had been sent to recover the Vietnamese kingdom for Gia Long from the Tay Son rebellion. Led by Pigneau de Béhaine, the expedition was cancelled by an officer in Pondichéry. Pigneau still went ahead with his own money and managed to help the vietnamese king significantly.
Now say this goes through, the French army actually gets into Indochina before the 1800. At the death of Gia Long (maybe earlier than OTL), it's turned into a Protectorate during the Napoleonic wars. Using this base, and with the complicity of the sultans of Mysore, manage to get a solid foothold in India. With a huge diplomacy effort, the manage to overturn the alliance system of the Brits.
I imagine a lot of Indian kingdom were not happy with the British land grabbing and the way the Benghal famine was handled. Wiggle room there.
That's more outlandish but maybe some elements of it are not completely ASB? The help of Mysore in particular seems like a solid PoD. Maybe if Napoleon manages to ally himself with Oman as well?