So it all depends on how Britain and France do? I can see France effectively giving up the colonies until the negotiations.
France would instead concentrate on trying to win the valuable spice islands off Britain - bear in mind that our POD was France winning the 7YW anyway so we are expecting France to be stronger to some degree in this TL - and the colonists won't get involved in the Caribbean. It's entirely feasible that the French would do better overall than the British, and then London would have a tough choice between giving away its very profitable islands, or telling the colonists to clear off the far-far-less-valuable Ohio lands. Bearing in mind that London already had taken issue with the colonists' disregard for national boundaries and their willingness - even, intention - to mistreat their neighbouring states (native and colonial) means that they by no means would necessarily support the colonists in the peace treaty (which the colonists would have no representative at). On the other hand, they may choose that the lesser of two evils is reduced profits in exchange for eliminating a source of conflict for the colonists. Of course, another equally plausible option is that the Royal Navy is just too strong for France and Britain wins the war and makes its own demands - but it's not a foregone conclusion, not at all. This stuff is entirely up in the air to be honest, and is the kind of thing where, if you were writing a TL about this, you could essentially choose the course and the winner of the war yourself without much complaint, so long as the campaigns made logical sense.
Bear in mind, in case you were thinking about it, that Britain refusing to support its colonists and essentially turning round and telling them "leave Ohio now and play by the rules!" would upset the colonists yes, but a major factor in securing their loyalty was the threat of a large French colony on their borders. If the French retain their North American possessions, the colonists are likely to be too nervous of reprisals to risk attempting another ARW - so the British siding with Caribbean status quo and telling the 13 Colonies to stop expanding into their "claims" would not likely instantly spark a declaration of independence, counter to what some here may suggest.