You're probably overthinking this, as the actual price will depend more on the route, the time, etc. than the airline. It's probably best to just check the price for your specific journey and book the cheapest tickets you can find. If you don't mind a longer travel, you could also use some search engine that will consider many airlines and indirect routes.
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 fares on regular airlines as well. If it happens to offer a good price on the day you want to fly, there is no point avoiding Air France because it is the most expensive in general.
For example, looking at some random date in November, I can find one-way flights to Dublin for about EUR 80 with both Air France and Aer Lingus. Ryanair won't always be cheaper and if that's too much, you should really consider some other means of transportation like the bus (and even then, I am not sure it would that much cheaper).
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. Also, Ryanair actually does not fly from Paris (or most “real” airports) but from alternative airports (in this case Beauvais or Châlons-en-Champagne), which are often more difficult to reach.
Regarding luggage, it's difficult to compare directly but all three airlines charge for hold luggage, at least for some fares, and impose an extra charge for overweight luggage. See the rules for Ryanair or Air France.
