Sorry, but what's an OTA? If you mean things like Hotwire, I checked those.
I named those not because they were the only airlines, but because the time and cost best suit our needs. I know Easyjet Ryanair Vueling etc. appear to operate this route (CDG/ORY - BCN) but with our baggage requirements, it ends up being even more expensive. Also the high speed rail seems to be more expensive than what I just noted, unless I'm missing something.