Two things:

1) I don't follow what you mean about the metro being inaccessible - there are several metro stops around the Champs de Mars and even on Bastille Day (in my experience) there isn't a huge crush.

2) Paris is an easily walkable city. You could stay anywhere in the 5th, 6th or 7th arrondissements without much of an issue; at a push, you could even stay in the 4th. It all depends on how much you like to walk (and on the weather, although if it is raining you would probably not be out anyway!).