Not necessarily. In fact, Muhammad Ali Pasha probably wouldn't be in Egypt during this alternate timeline. If Trafalgar isn't the disaster it has been in OTL, then the French can very well remain in control of Egypt. It was Trafalgar that allowed the British and Turks to eventually oust the French. Secondly, Muhammad Ali isn't an Egyptian. He's an Albanian, sent by the Turks to regain control of the area following the french defeat. Hence, no french defeat in Egypt, no Muhammad Ali Pasha in Egypt. Even assuming the French are still ousted out of Egypt, Napoleon would return after peace in Europe had settled. If only for the fact that Egypt was HIS conquest, one that brought him tremendous prestige, that had incredible value in terms of scientific and cultural gain, the grain of Egypt shipped back to France would have value too, not to mention that Napoleon foresaw Egypt as his door towards the Orient. He had his eyes set on Syria (the christian population there being seen as a natural support, and he would have liked to add King of Jerusalem to his list of titles probably) which he saw as a launching base from which to threaten British India - through Mesopotamia and Persia if necessary. Back when he was a general trying to conquer Egypt, he actually had dreams of recreating Alexander's Empire.
I am actually surprised that in this proposed alternate map, the French don't have control over the whole of Syria. In a scenario where the French defeated the Ottomans, Napoleon would have demanded not only Egypt, but also Syria. Alternatively, if the French don't have Syria, that means history went as normal - Napoleon conquered Egypt but was stopped at Acre by British and Ottoman forces, fled Egypt, and did not return. With Trafalgar not a total British victory, the French could have held onto Egypt and the Ottomans might have acknowledged their occupation of the area. But its probable that the British could not have landed in Syria, and Napoleon would have reduced Acre before going back to Europe smelling another European war - thus stopping his conquest short of his initial gambit - either marching to Constantinople from Acre, or to Bagdad. This is, incidentally, the scenario from which I think is more probable that Napoleon would not extend his conquest in the Ottoman Empire. If the French conquests in Egypt and Syria were acknowledged by the Sublime Porte, rather than taken back, and peace stabilised in the region, Napoleon would not see an automatic need to return to the area, especially with the British already destabilised. On the other hand, if the Ottomans had driven the French from the area, with peace in Europe, Napoleon would probably return, and this time he would not settle for just Egypt and Syria - he would bring the whole Ottoman Empire down and make it a puppet state. And he would succeed, because with the British out of the way, and with the Russians friendly, no one could hope to stop the French from doing what they want vs a decaying empire.
On another note, I also think, as has been proposed before, that assuming a British collapse in North America, Quebec would be a satellite of France and would probably have cores over Ontario and New Brunswick; especially since with British loyalist migration out of the area, french population would be a majority there.