If Napoleon dies in Egypt, the Directoire will be overthrown by some other general, but maybe by a less ambitious one. Sieyes and his gang will be in power, which isn't bad if you want stability and a competent government.
I see the constitution of Sieyes being enacted: this means the rule of a litte group of persons, but avoids Napoleon's personal rule. France will stay a republic for at least another 10 years.
Since Napoleon is a good, but not the sole good French general, French expansion in Europe will continue but without the disatvantages of Bonapartist imperialism. With the installation of republican regimes in the conquered territories, France will surely gain the support of the local population and be able to expand such as the Empire did OTL.
The hardest challenge for France without Napoleon will be Great Britain outside and the democratic opposition inside of France. Especially the latter will claim for direct elections and control of the government by the people, two things Sieyes, Ducos, Fouché etc. not want to let happen.