I just returned from a stroll to check out this "festival", which consisted of a single food truck and a 3 person band in Jubilee Place and the usual Saturday traders in the Green Market (though some with small cardboard signs in their stalls saying "Bastille Festival", I guess to remind you why they were open on a Sunday, as there were few indications otherwise that there was a Bastille Day celebration happening).
Perhaps it gets better at night, but given London's proximity to France and the space available at Borough Maket and its orientation towards food, I was very disappointed with this event. If you're looking for a festival, or even French food, keep your expectations low. This certainly wasn't what I'd expect from something that was billed as "London's largest Bastille Day celebration" (as stated on the Better Bankside website).
I went a few years ago and had a pretty good time. If I remember, it wasn't actually in Borough Market but on Park Street. The road was closed and there were food stalls, face painting, some performances and plenty of food and drink. I think it was sponsored by the President cheese company as we came home with lots of samples and money off vouchers.
Almost gave up on watching the Wimbledon final on Sunday to visit so looks like we made the right choice!