My starting point for any search is always "ITA"... matrix.itasoftware.com
Quite easy to use at a basic level and there are some "advanced tutorials" here on FT...
Yours is a very simple search (as you ARE looking for direct non-stops...

..rather than ORD-FRA via KTM, AUK and JNB..

)
You can start by just entering (say) ORD in the
from and FRA (or wherever) in the
to and playing... there are syntax options available to speed things up too.... but I'm no expert on those... simplest way to search more than one European desto would I think be using the "or any airport within X miles" feature....
I'm sure you'll get some better advice here... Good Luck with it...
P.S. On a simple ORD-FRA search out Aug 10 and back Aug 17 ALL the cheaper options had one stop....