After obtaining the seventh gym badge in Pokemon X, do I have to chase after Team Flare and if so, where?

Question

If yes, could the answer be as specific as possible, if not, could the answer please indicate where I need to go and what I need to do?

Answer 1

If I remember correctly, you need to go to the red-colored café in Lumiose City. It's near the Pokémon Center on Magenta Plaza. A Team Flare member should be standing outside.

Once inside, you need to talk to both waiters and defeat them. Then interact with the bookcase in the back to open a hidden door. From there I suppose you can figure out the rest. :P