We recommend searching flights to either Gothenburg, Sweden (GOT) or Oslo, Norway (OSL). Gothenburg airport is about 190 km from Bengtsfors and more suitable if you search flights from within Europe. Oslo is a bit more than 200 km from Bengtsfors and has more international destinations to offer.
Connections:
From Gothenburg (GOT) you'll have to take the airport shuttle to the railway station Centralstationen in Gothenburg center. From there you can search fro train connections to Bengtsfors - sj.se
From Oslo you can search connections to Bengtsfors on vy.no.