First, how much $ or euros are we talking here?
Also, try this - fly to Frankfurt first. I remember paying about 20 euros for this flight about 2 years ago. Then get tickets from big/cheap airlines that fly regularly from Frankfurt to the US. Few that come to my mind are Air India, Cathay Pacific, Delta, American Airlines and such. If flying directly to Minneapolis is expensive, choose other airports as your port of entry and then get another plane to take you to Minneapolis. Seattle, Denver, Milwaukee, Phoenix, Los Angeles, New York, etc all can be good options. I think I paid about 500$ to fly from Frankfurt to Denver in June (can't remember the airlines). Just keep looking.. you'll get a good deal.