What is the best way to get from Seattle to Arles France?
The closest airport to Arles is Marseille (airport code MRS), which is a major airport receiving flights from lots of places. There are no nonstops from the US, but you should be able to get there from Seattle with one connection. If you can fly from Vancouver, investigate that as well.
Are you only going to the Arles region, or are you seeing other places on this trip? If you are, be sure to fly open jaw, into Arles and out of somewhere else. To find these flights, use the "Multi City" option on Kayak. Don't look for two one-ways, as that's much more expensive.
If you want to look at flights from both Seattle and Vancouver, you can put "SEA,YVR" in the search box (without the quotes, full caps, comma but no space between them). This will pull up both airports.
I've done the trans-Atlantic flight with a connection to Marseille airport several times. On Delta/AirFrance-KLM it costs about the same as stopping in Paris or Amsterdam. Air Canada is not such a good deal, charging several hundred dollars more for the second leg, which has to be on an affiliate airline. (The $Cdn is a bargain for you right now, though.)
Serving the region of Provence, the airport has a little train station with direct service to Arles so you don't have to go into Marseille to the main station. The regional train is nothing like the sleek high-speed trains but it will get you to Arles in about 40 minutes, with departures every 90 minutes or so. The SNCF train schedule site shows it as a one-connection service. That means there is a shuttle bus in front of the airport terminal for the five-minute ride to the train. It used to be that tickets were only sold by machine, a problem for American credit-card holders, but the airport website now specifies that there is an agent at the station. Or you can buy on-line, asking for Marseille Provence Airport. No seat reservations available, and paper tickets must be validated in a stamp machine before boarding.
http://www.marseille-airport.com/access-car-parks/access/trains