My considered opinion, having done it both ways, is to seek an "Open Jaw" reservation. Both Laurie and Dave, above, are correct. But, IMHO, my way is more convenient. Also, it ought not cost much more...
1. Fly ORD to CDG. Both AA and US have regular flights. You can connect on IB through MAD. I know it seems counter-intuitive, but it is actually smoother this way, at least IMHO.
2. From the baggage reclaim area, go outside and take Line #4 of the Le Bus Direct to Gare Montparnasse. Pay the driver. Ride takes @ 45 minutes from airport to train station.
Cars Air France” have become “Le Bus Direct”. Paris Aéroport is launching a new quality service, “Le Bus Direct”, in partnership with Aérolis.
www.parisaeroport.fr
3. From Gare Montparnasse, take the SNCF TGV to Bayonne, you can book here...
Buy train and bus tickets for the UK and Europe. Simple, fast booking.
www.raileurope.com
OR
Your gateway to the latest offers and news from SNCF, a global leader in passenger mobility and freight logistics.
www.sncf.com
High speed train takes about 5.5 hours. The scenery is beautiful.
4. At Bayonne, transfer to the TER #62 line from Bayonne to Saint Jean Pied de Port. You can buy your ticket from Paris to SJPdP at the Rail Europe or SNCF sites above...
Here is the TER schedules site:
www.ter.sncf.com
Also, in connection with arriving this way, I always recommend booking two night stay at SJPdP. The first night you will be tired from traveling for a day. Spend the intervening day to explore the town, exercise your legs, and top up supplies.
You can also arrange to send a suitcase or duffel bag, ahead all the way to Santiago using Express Bourricot. Send all the souvenirs you just bought at SJPdP and post-Camino clothes and supplies ahead, to be waiting for you. Two people can share one bag. Here is their website:
www.expressbourricot.com
It is NOT cheap. But it is easy, safe, secure and reliable. I use it every time I start from SJPdP.
5. AFTER your Camino, returning from Santiago, you can either fly, train, or bus to Madrid. IMHO, flying is the easiest. However, if you want to spent some time in Madrid, then the bus or train is definitely the way to go as these two methods land you directly in the city. As is mostly the case, large airports are well outside the downtown core.
Check routes and schedules here:
ALSA (bus) -
http://www.alsa.com/en/web/bus/home#
RENFE (train) -
http://www.renfe.com/EN/viajeros/index.html
6. Return home from Madrid, MAD - ORD direct. Easy peasy...
The bus and train ride from Santiago to Madrid is about 6 hours +/-. So, you likely need to plan at least one overnight at Madrid before heading to the airport.
OTOH, flying can be done in one day. You take an early flight out of Santiago to Madrid, then connect to your US-bound return flight. They mostly leave between 1100 and 1300.
If flying back, and NOT using Iberia or AA, consider that you will have to change terminals. IB and AA dominae T-4. Other US carriers, DL and UA, use terminal 1, IIRC. Allow an extra hour for making the terminal change, just in case.
The other advantage of using AA or IB through T-4 on the return is that your checked baggage is routed through to ORD. You do not see it after Santiago, until you arrive at ORD.
Hope this helps.