It's a bit tough to say because the changes that would allow the other European powers to really scramble for India could also change the balance of power in Europe and therefore change the players involved (FWIW, I think Britain being badly defeated but not so bad that it can't recover in the 7 years war would be a good start).
Still, there are some potential safe bets that can be made:
Wherever Britain goes, so does France. Better luck for France during the Carnatic Wars could see them take large chunks of India's east coast, particularly the Southeast.
Portugal could formalize holdings over a much wider hinterland than OTL's Goa as part of deals with the more powerful European militaries, as per OTL in Angola, so there goes a big chunk of Southwestern India. The Dutch could formally annex Sri Lanka as well. It's probably a stretch, but I could see Russia projecting power as far as modern day Pakistan, though they would probably be ruling through local proxies rather than directly.