Basel/Surrounding French towns

Mark,
Depends how much time you have. Colmar is very nice, but that is a full day trip. Some suburbs of Basel are in France, but they are uninspiring. You could visit the "Dreiländereck" monument, where the 3 countries meet, except that you have to walk through the docks to get to it it is not quite in the correct place because the correct place is in the middle of the river. Info here

I would suggest you spend your time in Basel. Go to the look-out by the cathedral (the Pfalz). From there you can see France and Germany.
Lots of Basel photos here, the first one is Basel SBB station: http://www.birswilly.ch/Baslertour2011.html

P.S. Make sure you know which station in Basel she is arriving at, there are two:

• Basel SBB for trains from Switzerland, France and Italy.
• Basel Badischer Bahnhof for trains from Germany, except IC and ICE trains (including those from Frankfurt) stop at both.

I've only been through it on the train, but Mulhouse looks pretty: http://edu-geography.com/data_images/countries/mulhouse/mulhouse-09.jpg

You can Google for additional pictures.

Trains are frequent and take 18 to 31 minutes. It appears that the RR station is a short walk from the old town. There may be closer, smaller towns, though, that would be equally nice for a short visit.

Edited to add that the trip time I gave above is from the Basle SBB station. If connecting from the other station, you'd probably need over an hour to reach Mulhouse, a much less attractive prospect.

Thanks for the advice. We will be coming from Frankfurt on an ICE. Our thoughts were to have breakfast in Germany, lunch in France and dinner in Switzerland. That's surprising there's nothing in France close by worth seeing.

Mark, there are places to visit nearby in France, Mulhouse, Colmar, Strasbourg, Route du vin d'Alsace, Haut Koenigsbourg castle, etc.
The problem is you are constrained by time. They are take 1-2 hours to get to, and you are arriving in Basel "mid morning", and need to be back at Basel station late afternoon (you don't exactly say when). You don't have enough time to get there and back, and have some time there.
There is plenty to see in Basel, which makes best use of your limited time. Another option is to travel from Frankfurt to Strasbourg, spend some time there, then get a train from Strasbourg to Basel later in the day (takes about 1½ hours).

But, Basel has plenty of attractions, a lovely old town, a cathedral etc. and you will make the best use of your limited time.