We've seen a few threads heareabouts which suggest it was a mistake for France to help the American colonists gain independence, because all they got out of it was a major power in North America that was hostile to the British Empire instead of a loyal French puppet.
I'm not quite sure how you game this out. A France that doesn't join the War of Independence wouldn't change much until 1778. Prior to that point France was providing weapons and supplies to the colonists, which seems like an obvious tool. Why would France, even if it's penny pinching, not want to tie down its enemy?
After Saratoga, the British were prepared to offer the Americans everything "except the word independence." I will grant that if the prospect of French intervention recedes, and the British are faced only with a grueling slog for years, maybe their terms become less conciliatory, but there's a limit here.
Don't you end up with Benjamin Franklin meeting in London with Lord North, to hammer out a deal?