When I was a teenager, low cost in French only applied to airline companies. The famous orange and white planes were launched in 1995, which is probably the cause for the sudden surge in this Google Ngram Viewer chart (French corpus):
Nowadays, you get voitures low cost (low cost cars), maison low cost (low cost house), etc. What puzzles me, however, is how the second word, cost, was adapted to French phonology. The French system has both /o/ and /ɔ/. By far the most likely phoneme if cost were a French word would be /ɔ/, as in accoste, poste, Lacoste, etc.
If French speakers had picked the phoneme whose pronunciation was closer to English cost, they would have chosen /ɔ/, like they do in the following loanwords: hot dog, Lost (TV series), job, stop, etc.
Now where do we have /o/ in English loanwords? Road (trip), (mobile) home, toast, etc. So, the only logical reason why the French pronounce cost with /o/ is that they get the English grapheme-to-phoneme mapping wrong, i.e. they probably think cost is pronounced like coast in English. Of course, this kind of approximation is quite common (think of sweat (shirt) pronounced sweet) but with cost it is really the unexpected, non-default solution. And as I perceive it, it is an attempt to associate foreign (albeit phonologically erroneous) overtones with this word. Oddly enough, the near-synonym discount has had a totally different fate; it is regularly pronounced à la française: /diskunt/.