In October, we will fly in and out of Frankfurt. We will have 10 days and are renting a car at the airport. Is it feasible to spend time in the Mosel valley and then drive to Alsace, France? Don't know how to divide up the time we have. Any help is appreciated!
Driving across those particular borders is no problem and with no border checks. Driving time should not be bad, such as from Trier to Colmar in 3-4 hours. Try www.viamichelin.com for routes and tolls associated with any faster French roads. The International Driving Permit from AAA includes translations in several languages, to accompany your state-issued driving license. See general driving tips at http://www.ricksteves.com/travel-tips/transportation.
I would say at minimum of 3 days to see Colmar and drive the wine route, visiting the villages, then a day for Strasbourg. Alsace borders the Black Forest so you may want to make time for that too. That area is not large, so it's easy to base yourselves in a B&B in one of the villages for the entire stay, except for Strasbourg.
I can't help with the Mosel segment.
I particularly like Obernai in Alsace as a base. It is a bit larger and has a bit more going on than many of the smaller places.
I don't know if you have any interest in military history, but Fort Mutzig is quite an experience. There is also Struthof Concentration Camp.