Yes, Napoleon did conquer Cairo as well as Alexandria when he led an expedition to Ottoman-held Egypt and Syria in 1793.
It was the primary purpose of the Mediterranean campaign of 1798, a series of naval engagements that included the capture of Malta. The campaign ended in defeat for Napoleon, and the withdrawal of French troops from the region. Napoleon believed that by cutting off Britain’s trade with India, that passed through Egypt at the time, he could have dealt an economic blow to the British isles, but his plan did not work in the long run as the British and their Ottoman allies fought hard against the French and won.
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