Tap Air Portugal has round-trip flights from Chicago (ORD) to Madrid, Paris, or Barcelona (MAD, ORY, BCN) for $354-$376 with a connection. Flights November to March.
Carry on bag with a maximum weight of 17.6 lbs is allowed for free on TAP. You can avoid seat selection fees by accepting the randomly assigned seat at the gate. Upgrading to a higher fare class that includes a carry-on bag for $65 may be cheaper than booking the “Discount” fare with the added $95 carry-on bag fee.
Flights on TAP allow for a free stopover (up to 5-days) in their hub city. This will be useful if you want to spend time exploring Porto or Lisbon before heading to your final destination. Link: More details on the TAP stopover program.