The 2E lounges are 50 euros. I believe it's possible to be denied entry due to crowding, and I don't think FFP membership will matter. I suppose they may be able to accommodate you at 2K if 2L is full (2M closes early I believe), you can ask.

But I might be more inclined to use the Arrivals lounge in 2C landside for breakfast and a shower after the redye (it'll only be 35 Euros after 10am), and then just have dinner in Paris before heading back to the airport in time for your flight.