French was a language&culture status of educated upper-class person. Namely- a nobleman (dvoryanin). You can look in to opening chapters of Tolstoy's "War and Peace" for illustrative example how deep French culture was seeped in to aristocracy's life.

The thing is, that you apply modern mentality to nobility. Nationalism (ethnic or politic) was not a thing to them, and Russians are not exception of general rule. The fact, than Russia few times was at war with France simply did not translate in to "hate all things French&Western" to them.For a noblemen, a Napoleon was usurper anyway, so defeating him and marching in to Paris, they helped rightful king of France to regain throne.

As for anti-Western sentiments Crimean War left much larger impact. Napoleonic War actually inspired a number of officers to demand things like constitution and other western noncense (so-called Decembrist revolt- all major participants were veterans of 1812). To hire French gouvernante was a must for any self respecting dvoryanin with children during entire 19th century.

All in all, Fench was the cuisine, language and culture of a nobility and upper-class all across continental Europe at the time (we still have term lingua franca as a remainder of that ere), and Napoleon did not changed that for Russian dvoryanin.

But French food remained popular regardless." Or is that really all there was to it?

Among whose who could afford it. It was still a culture of aristocracy and upper-classes.