Lots of countries do this, not only France. Military parades are an easy way to remember and commemorate the fallen in battles, and to remind the civilian population of the magnificent army protecting them.

But to your other point, yep, the French Fifth Republic has a very strong President figure (not a monarch on a few important distinctions like succession, but still). And after the failures of the Third and Fourth Republics that showed that compromise is complicated to achieve and without a strong position somewhere there is just pure chaos and instability, it was the only way forward.