Foreign pilots with Finncom have been on contracts only, a friend of mine from Fly Niki amongst them. You would be expected to learn Finnish.
Finnish CAA will only validate a non JAA ATPL for 1 year with a JAA initial Medical. Validaton is NOT renewable thus you need to complete all 14 JAA ATPL subject exams add LPC (Licence Proficiency Check or sim check as you know it in US) in the type you fly to be issued an JAA ATPL
Further you need to obtain an ICAO language assesment to level 4 standard. FAA english proficiency does not give you credit.
Hardest part would be your right to work status. As your better half (assumption) is Swedish, this will allow you to apply for a Schengen D-visa or temporary residence permit, that is valid only for work and residence in Sweden. It does not allow you to work in any other Schengen country.
With the present situation with unemployed pilots around Europe, getting a sponsor is virtually impossible.
My recommendations: Find out about the FAA-JAA conversion. Get it done early in the game. Obtain your Swedish temporary residence permit. With that you are legally eligible to work, study and live in Sweden. There are ways you are also allowed to work elsewhere in Europe but the process is too complicated to explain here. We have ust gone through this with my wife, a non-eu citizen so it's all fresh in memory.