Before or after the Egyptian campaign, where then merely General Bonaparte attempted to relieve them of a province, squashing the Turkish soldiers there with contemptuous ease, cutting metropolitan Turkey off from most of it's imperial claims, and lunging north for Judea and Palestine, only stopped by amphibious counterattack by the Royal Navy?
They were long term enemies of two of the key elements of the anti- French coalitions, Austria and Russia; naturally they should have sided with Napoleon, but French revolutionary thinking was no more to their taste than Europe's, and after the Egyptian campaign there was too much bad blood, in addition to how impressively they had been thrashed.
No friends on either side, nothing to gain, and out of their league anyway without major army reform that they could not afford and hardly dare attempt in an age with revolution in the air.
So...back up a bit. How do you get things to play out differently so that they do get involved? The Egyptian campaign needs to not happen for a start, which considering how central it was to long term anti British planning, means major changes in French thinking.
How do the French get the Turkish on board as allies? Bribery, promises, threats, what? How this is done determines how well it will hold together, which will be important if there is going to be a joint Franco- Turkish attempt to march to and take India.
Hmm. This could be fun.