I have a US passport, and I have often entered Germany in Frankfurt. I agree with bacchus85, you should have no problem. I have rarely had to wait more than 10 minutes for immigration in Frankfurt, and the luggage generally arrives within 20 minutes or so.
I did miss this window once, when United could not get one of the cargo doors open on a 777. After 90 minutes, they sent all 60 people to fill out lost luggage claims... But if you want to plan for every eventuality, you would have to plan for a train the next day!