British Airways has round-trip flights from Austin (AUS) to most major cities in Germany (TXL/FRA/MUC/HAM/DUS) for $526-$560 with a connection. Flights October to March. 7-day minimum stay required.
New Years Eve is available if you can do a 10-day stay or longer.
Carry-on bag is allowed for free, but there is a fee for seat selection and checked-bags. You can avoid the seat selection fee by accepting the randomly assigned seat at the gate.