Not sure, but sounds pretty iffy to me.

arriving at Sea-tac at 5:45 does NOT mean you are OFF the plane at 5:45 so allow at least another 15-20 minutes or so to get off. With that in mind, doesn't sound like you have enough time to get bags, stand in documentation line (sometimes very long) recheck bags (possibly at another terminal) and be on the next flight by 7:ish. If you haven't made the reservation yet, I'd take a later flight out of Seattle. If plane is at all late leaving Paris, you will absolutely not make it.

Okay, I'll go with the later flight ... thanks for the input!

The problem with that arrival time is that it's perilously close to the typical arrival time (i.e., late) of BA's 747 from Heathrow. If you're unlucky and hit immigration at the same time, you could be in the passport queue for half an hour or more (if on a US passport, longer if on a foreign one.) Then you have to wait for bags to arrive, then walk through customs to the bag re-check, where the bags are put on a conveyor that will take them either to the main terminal carousel or to the connecting flight if they're through-checked. Icelandair and Alaska are partners, so they ought to be tagged to Redmond, but if not then you would need to ride the train to bag claim, re-collect your bags, then go upstairs to re-check them at the Alaska counter, go through security, etc. - by which time you'd probably be cutting it awfully close for the 7:30 flight, if not missing it. Now this of course assumes that your Icelandair flight is also on time (or indeed that the Horizon/Alaska flight is on time) but you can't afford to gamble on such things.

If there's a later flight I'd opt for it.