Please list that 'double digit' number of airlines that fly between Paris and London. I get to max 7 (British, Air France, easyjet, Vueling, Transavia, flyBE, cityjet)
There's no shortage of other airlines selling the BA, AF or Vueling flights under codeshare agreements as a leg of another journey, which is one of the main reasons why demand on that route exists. Iberia and airBerlin sell others' LON-PAR flights under their own code as a point-to-point flight too. Not to mention the daft indirect itineraries you can buy if there's really no other alternatives