Any suggestions for a carry on for Ryanair? I would like the bag to be as big as possible and still meet Ryanair's requirements.
I had this same issue while planning some intra Europe trips this summer. I found this http://www.ryanair.com/us/questions/samsonite-cabin-bag/. I have no personal experience with the bag because I ended up not booking with Ryan Air.
Ryanair and the European budget lines in general not only are very clear on what bags allowed in the cabin, but also check them diligently at the boarding gate. You may pay a hefty premium if your bag is taken away at the gate to be stowed in the belly of the plane. It's wise to read the website regulations and make some effort to follow them.
If you are using RyanAir for travel to of from Paris, be aware that they use a small very small very remote airport at Beauvais, half of the way to England.
As Nigel points out you've got to go to Ryanair with your eyes open. To get the best deals you've got to play them at their own game, where the odds are stacked against you.
When Ryanair is mentioned I am reminded of this Fascinating Aida - Cheap Flights.
Be advised they use words that some may view as strong.
If you possibly can use Vueling or Easyjet, both budget airlines that use regular airports and have reasonable luggage policies (precise, but not hugely different from legacy carriers). Ryan Air uses inconvenient airports in addition to having onerous baggage policies.