There's an incredibly lengthy (and unwieldy)
thread for using US miles on Star Alliance partners. You can get some good advice in there...particularly if you get into a jam. If you're a do-it-yourselfer, then I highly recommend this exercise because routing an award can be a bit of a 3-dimensional jig-saw puzzle, and it's satisfying to solve for it.
The fact that you're willing to travel in economy is useful because there is likely to be more availability.
For a beginner I recommend using united.com to search for Award flights because it does a pretty good job of finding creative routings all on its own. If a flight turns up as available in the Economy Saver Award column on united.com, you should be able to book that flight using your US miles by calling US and giving them the flight information. Be forewarned that dealing with the US agents 90% of the time involves taking them segment by segment through your itinerary (e.g., If you tell them you want to fly IAD to BCN, on July 9 they will tell you that their computer doesn't see any availability. You'll have better luck if you ask them to check segment by segment for the routing you found on United's website.) Using July 9 as an example, United tells me you can get from IAD to BCN via YYZ on Air Canada or via FRA on United & Lufthansa.
There are other tricks and tools you can read about in the thread I referenced (ANA, Expertflyer, AC), but for a simple Europe trip I think you can probably find what you want on United's website.
The other rule of thumb is flexibility: if you're not finding what you want, try reversing your itinerary (into CDG out of BCN), or try breaking the connecting flights down and looking for originating flights from other gateway cities on either side of the pond such as PHL/EWR/JFK/BOS or LHR/FRA/ZRH/MUC/etc. and then see if you can find a flight that connects from your desired destination to one of those cities).