Are there any smaller (cheaper) airlines that fly from Iceland to Europe, particularily Paris?
I've only flown with Icelandair...that would be my top choice from KEF to CDG. You could look into Iceland Express. There are other budget and legacy airline options available, but you may need to connect somewhere else in Europe first before landing at CDG. Maybe check the airfield's website (KEF) and see what airlines they have listed.
You need to look at the online flight websites, and plug in the info. The best reason to go through Iceland is to see their beautiful country and beautiful people. And Icelandic Air will often allow free stopovers. I've not found Icelandic Air to be especially cheap on flights from the U.S. to Europe, and they just have a few U.S. gateway cities. My nephew was stationed in Iceland with the Marines, and they hitchhiked everywhere. The drivers would ask when and where to meet so they could take him back to his base later. That's a different country.