If you are a military history nerd, the Musee de l'Armee (Les Invalides) is a must. I had a single afternoon in Paris and that is where I went. It was not enough time to see the museum - I could have probably spent several days there. Since my specific interest is late medieval and early modern armour and weapons, I spent my time looking at their armour collection, which is among the best in the world. This includes the armours of multiple French kings, including Francis I, Henry II and Henry IV as well as high quality armours from other sources. There is also a truly stupendous collection of artillery dating back to the Middle Ages - including 15th century forged bombards and some very early cast brass pieces from the turn of the 16th century, as well as a tremendous quantity of later artillery. But this is only their early collection. They also have an -extensive- Napoleanic Wars exhibit, and large exhibits on both world wars and more contemporary conflicts.

If you have limited time I would plan out which sections of the museum you want to see and admit to yourself you won't see it all. Focus on the period that interests you most.

As far as the crowds, there was a bit of a line to get in, but it wasn't too bad - security was tight but even then the line wasn't more than 15 minutes long, and once we were in the crowds were not too bad, and we went on a weekend.