Don't do it... You will have to collect your bag in Madrid. That's Madrid's weakest point, though not that bad in T2, expect 30 minutes wait. You then need to take the bus to T4, it leaves every 10 minutes and takes about 10 minutes. Check-in in T4 will close 45-55 minutes before departure. I suppose you'll be fine for the 22:05 flight, but do you really want to wait around that long?! You'll also have to collect bags in CDG, but I'm not sure which airline you're flying?

How does the $226 for the one way work out? That seems cheap for AF and IB on the same ticket, unless you are looking at Iberia Express connecting to Iberia? Have you looked at booking with Air Europa? They codeshare with AF on CDG-MAD. Your bags will be checked through and you can connect in no time in MAD.

Can't you have an open-jaw ticket USA-LCG, PAR-USA? Or even just to MAD? USA-LHR, PAR-USA?