Icelandair has round-trip flights in their “Light” fare-class from Dallas (DFW) to Paris (CDG) starting at $366 with a connection. Flights January to March. 5-day minimum stay required.
Note: Carry-on bag is allowed for free, but to check a bag will cost +$75 more each-way. You should be able to upgrade to a “Standard” fare-class for about +$100 more, which allows for a free checked-bag.