Well, nowadays a lot of solid-state theoreticians consider themselves to use QFT to some extent. Is there some specific subfield of solid state physics you are interested in?
Without further hints, I suppose the group of Antoine Georges at CPHT (belonging to the CNRS) uses quite some QFT. Their research focuses on using dynamical quantum mean field theory to study strongly correlated materials. I am not quite sure about the groups at LPMMC or Institut Neel. I think the group around Guillaume Malpuech, focusing on light-matter interaction in low-dimensional structures might also use QFT to some extent.
However, you might want to have a look at the CNRS website yourself to find what you are looking for. It is quite huge and complicated, but as research in Paris is pretty much centered there, you will find what you are looking for sooner or later.