There were two key events in the "occupation" of Egypt. One was the takeover of Egypt's finances (and essentially the entire apparatus of government) and the other was the actual occupation of the country predicated by the Urabist revolt and following the bombardment of Alexandria.

In regards to the first event, the French did "occupy" Egypt in a sense. Egypt's terrible finances in the late 19th century, caused by over-borrowing at exorbitant interest rates and the collapse of cotton prices following the return of American cotton production to pre-civil war levels, led to the establishment of the Caisse de la Dette in which European countries holding Egyptian debt, primarily Britain and France, took direct control of the finances of the Egyptian government.

This, along with a host of other complaints, including proto-Egyptian/Arab nationalism, led to the Urabist revolt which saw Ahmed Urabi essentially take over the Egyptian government (the exact machinations by which this occurred were complex and not really worth getting in to here for the sake of your question. Urabi is a fascinating figure.) Suffice it to say that the Khedive, the titular ruler of the country was left powerless in his own government.

The British and French issued a joint ultimatum to Urabi requiring the Khedives position to be re-established. The note was unbelievably heavy handed. Combined with the presence of British and French ships outside the city, it sparked rioting in Alexandria primarily targeting foreign traders.

As a result the British, but not the French, bombarded the city.. While the British commons voted for intervention, the French could not get support for military invasion.

As for why that was, it's partly because of their other regional colonial interests. The French invasion of Tunisia the year before was costly and unpopular. Also even in this age of rampant imperialism, the case for invading Egypt was extremely tenuous. Urabi himself had European supporters, he was a populist and apparently quite charismatic.

The British also arguably had a greater interest in invading Egypt, as their concerns went beyond the canal. When American cotton went off the market during the Civil War, Egypt had become a major supplier to Britain's factories. Britain also wanted greater security for that supply, considering how painful the Civil War had been for British industry. It led to greater British control in Egypt, India and elsewhere.

Even though the British occupied the country, the French continued to be paid off has holders of Egyptian debt and were major shareholders in the Suez Company, which was based in Paris and a descendant of which still exists today.

Sources:

For a straightforward account of these events see P.J. Vatikiotis' History of Modern Egypt: from Muhammad Ali to Mubarak. For the broader regional colonial picture of both countries see Eugene Rogan's The Arabs: A History. For a first hand account of the events, including interviews with Urabi, see The Secret History of the Occupation of Egypt by Wilfrid Scawen. I haven't read it, but the Earl Cromer also wrote his account of the occupation, partly in rebuttal to Scawin, entitled Modern Egypt or Modern Egypt, by the Earl Cromer. The economic impact of cotton on the political events the unfolded is poorly studied, I actually very nearly did my undergraduate dissertation on it, but the picture can be discerned in Roger Owen's The Middle East in the World Economy: 1800-1914

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