Napoleon abandoned his army because he assumed the adventure was doomed. However, he did not become a pessimist until well after the British fleet sunk its counterpart. It was the Siege at Acre and the outbreak of plague that forced Napoleon back from a conquest of Syria and Turkey.
There are many good books written on the French left in Egypt, including one by Strathern. The army largely suffered as soon as it landed in a climate that was too hot, dry, and hostile for the French to adequately deal with. The army came well-prepared to win a set piece battle and feed itself. What the army lacked however were large numbers of cavalry, especially light cavalry essential for reconnaissance and requisitioning the countryside.
The French tried to make the climate less hostile thru cotton and paper. Napoleon applied his best efforts to win the 'hearts and minds' of the citizenry in Cairo, which included tens of thousands of pamphlets and other paper proclamations (invariably claiming Napoleon was actually there by invitation from the Ottoman Sultan who took pity on his people oppressed by the usurping Mamelukes). His successor by contrast did one even better, converting to Islam and 'going native'. But French efforts to become popular in the land they just conquered were tone deaf, inhibited by language and religious differences which led to peasant revolts mirroring the vast rebellion in Cairo that Napoleon had brutally suppressed before.
Once Napoleon left, things got weird. The British fleet, Sir Sydney, various Mameluke Beys, and the Ottoman military never gave up harassing and attacking the French in Egypt. There are reports of plague and famine, hunger and atrocities. It is a testament to the high-quality of the French army that with and without Napoleon, it generally won any set piece battles against either Egyptian peasant, Mameluke or Turk. However, when the British landed a large expeditionary force of European Neapolitans and redcoats, I think the French finally realized they were truly cut off from the homeland. There was no breakout attempt; just a tame surrender.
The survivors were repatriated to France at the end of the War of the Second Coalition. Surprisingly enough, there was less animosity against Napoleon for his desertion than you would think, likely due to his control over the presses and his ability to link his coup and French European successes as integral to the repatriation of the Egyptian expedition. But Napoleon also sent many of the soldiers back on another colonial misadventure, this time to Haiti where many of the soldiers died of Yellow Fever (which incidentally only arose from Africa in the 18th CE, which explains why Cortez and Pizarro succeeded where the French later failed). Perhaps Napoleon found them an inconvenient army.
Expanding on /u/DavidlikesPeace's comment here, since that's the main points covered. Just as a few side notes:
After Napoleon's failed invasion of Syria, the British handed over some letters and newspapers from France (which the French had not been receiving obviously) and Napoleon discovered the full extent of the war back in Europe. He said:
"“Fate decided against my dreams; I received letters from France ; I saw that there was not a moment to lose. I reverted to the realities of life, and I returned to Paris.”
Napoleon's departure from Egypt in August 1799 was planned in secrecy and few people were told until the very last moment, either because of the effect the news might have on army morale or because Napoleon's generals might have opposed it.
General Kléber woke on 22 August to a letter from Napoleon that basically said 'you're in charge now, goodbye and good luck' along with some advice for ruling. This advice included Napoleon's recommendation that should Kléber lose 1500 men to the plague, then he ought to make peace with the Ottoman Porte and abandon Egypt if necessary. He also promised to send him a company of actors from France, which he himself had been pestering the Directory for, since he believed dancers and actors would "begin changing the manners of the country."
The following year, 1800, Kléber was assassinated by a student in Cairo, and command passed to Menou. Menou was a bit of an eccentric and reportedly kept the Rosetta Stone under his bed for safekeeping. Menou made himself quite unpopular by deciding to end peace negotiations with the British and Ottomans, believing Egypt should remain a French colony.
A British-Indian expeditionary force landed in March 1801, and soon Menou retreated to Alexandria. Napoleon, now in power in France, twice attempted to send reinforcements. However, when the troops found out where they were being sent they either refused to depart, or turned their ships around half way there. However, the actors Napoleon had promised did finally arrive that summer. The British even offered to let this flotilla land in Alexandria, but Menou refused. Soon after, he agreed a truce with the British by the end of October 1801 the last of the French had left.
Sources:
I can't say for everyone, but the future Marshal Louis-Nicolas Davout left Alexandria during the evacuation in March 1800, and arrived in Toulon in May. On the way, he was accosted by a British frigate and interned in hospital for a month, having been told that the passport given him by Commodore Smith in Egypt were invalid and that he needed new ones from Admiral Keith. Then, he was captured by Tunisian pirates, although he was able to get past them by presenting the passport he had been given by the Ottoman Grand Vizier. Desaix, his companion during the adventure, went on to command a division at Marengo on 14 June, where his timely entry reversed the Austrian success but also cost him his life. Meanwhile, Davout remained quarantined (having left Egypt due to illness in the first place), and would not take up a field command until his promotion to a divisional general 20 days later on 4 July.
Source: The Iron Marshal by John G. Gallaher