Having a look at the TLS website, and taking tomorrow as a guide:
There are 112 arrivals - 67 (60%) internal French flights including 38 (34%) to Paris. Air France operate 66 (59%) of the flights.
Apart from the UK locos mentioned, European majors fly to the capital cities and there are a few flights to North African capitals.
TLS isn't really a major gateway to a popular region of France for Brits, so the scope for more UK flights looks limited. But if EZY wanted to take on Air France, they could try it here (if the French would use a non-French airline!)