You're overthinking this, just check the price for your specific journey and book the cheapest tickets you can find. If price is your only concern, there is no point agonizing over the airline as actual price can vary a lot depending on the route, the time, etc.
As a rule, the most expensive fare on an Air France flight will be more expensive than the most expensive Ryanair fare and conversely the cheapest Ryanair fare will probably be the cheapest overall but in-between everything is possible and there some very attractive fare on regular airlines as well.
Note that both Air France and (especially) Air Lingus moved towards “no frills” service on short-haul routes so you might have to pay for hold luggage in any case.