The most obvious routing to me is SLC-CDG-LIS on Delta/ Air France. But you don't have miles for that and it would be a hard get.
Most likely you Will have to make two stops. With two stops your options are close to limitless: connect in any domestic hub, connect in any european hub. As for what of those options are best, its silly to discuss in the abstract until you have available flights on the dates you want.

I'm not sure if you are saying these are all the miles you have, but you will be hard pressed to find 6 award seats on one flight