Trying this again.
Egypt was in heavy civil disorder prior to Napoleon arriving. The Mamluk elite were attempting to over throw Ottoman rule and the Ottomans had very little direct control over Egypt prior to Napoleons arrival. Mamluk forces numbers well into the 60'000, however the appeared a bit divided. In the battle of the pyramids, there was over 21'000 mamluk troops, though over 40'000 more Mamluk troops did not participate. Maybe they beleived Napoleon.
Napoleon had mentioned in memoirs that he considered the ottomans allies, however he also made declarations to the Egyptian people that he intended to free them from Mamluk and Ottoman oppression.
Napoleon wanted to put an end to British Indian trade and commerce that was bringing a significant amount of wealth to the British empire. The Maratha empire in India had opposed the British, however were ultimately losing. Napoleon wanted 12'000 french soldier in India to help his Maratha allies drive out the British from India once and for all. Of course, once this was done, Napoleon wanted French dominance in trade with India.
Battle of the Nile:
This was not Napoleons significant defeat in the Egyptian campaign...it was in fact a defeat, however at the same time the French were winning battles on the land in Egypt.
Siege of Acre:
If I can make a change to your question, I would instead ask 'what would have happened if Napoleon was successful in this siege?'. Acre was considered by Napoleon to be an easy conquest and they would quickly surrender which would then be a quick stepping stone to the holy lands and Napoleon's capture of Jerusalem. However, the French had previously sacked Jaffa and killed many in doing so...the defenders of Acre were quite aware of this and put up a stubborn defense. Napoleon could have been quite easily victorious with cannons, however he was forced to rely solely on infantry...a British fleet intercepted Napoleon's artillery on ships headed for the siege. The British then used these cannons to re-enforce the Ottoman defenders and used their gunboats to fire on French forces from the sea.
If you want to be more specific with the question...what would have happened if the British failed to intercept these cannons and Napoleon was capable of capturing Acre?
Napoleons end game:
Napoleon wanted two outcomes from his Egyptian campaign:
Establishment of a double port in Egypt, effectively connecting trade with India through Egypt. This would have been a precursor to the Suez canal.
Support the Maratha Indians and drive the English out of India. Napoleon idolized Alexander the Great and wanted to conquer his path into India using a similar route. The battle of Issus was Alexander the greats decisive win vs Persia and Napoleon would do the same.
What if he succeeded in taking Acre:
Napoleon would have (tried?) to raise an army including Mamluk and Turkish peoples and march through Persia and into India where he would join his allies and drive the British out. This would have been a harsh blow to the British economy and may have impacted their ability to amass the forces that were eventually victorious in Waterloo. Additional money and manpower from the newly acquired regions could have changed his luck in Russia as well. If it did...well, I'd imagine I'd be currently posting this in French.
That said, when Napoleon returned from the Egyptian campaign is when he engineered his coup d'etat and become emperor. Had he been successful in Egypt, the prolonged movement to India and the attack on English forces would have heavily delayed his ability to return to France. Perhaps he would never have become the emperor when he returned from Egypt if he went to India instead.