Coming on A6 from Mannheim: Exit Kaiserslautern West and follow the directions to Kaiserslautern, right after the bridge take a right towards A6 Mannheim but do not go on A6, follow the signs to Weilerbach. Take the first right in the circle.
When I searched the web for Kaiserslautern bicycle rentals (Fahrradverleih in German) the one address I came up with was Willy-Brandt-Platz 1, which turns out to be the address of the Tourist Information across from the theater.
The Tourist Information didn't have any bicycles to rent when I was there, but they did give me the names of two possible rental places. I didn't have time to try either of these, but I'll post them here for future reference and in case anyone wants to try them. (If you do, please let me know how they are.)
The first is Projekt Velo Kaiserslautern, 0613-37100606. This turns out to be a project run by the ecology program of the city administration. It is intended to provide work for unemployed young people, who work under professional supervision fixing up old bicycles that people have donated and then lending them out to local residents. To borrow a bike you have to leave a deposit of 75 euros, which is returned (but only if you have a German bank account) when you return the bike in good shape. The borrowing period is up to six months, and the customers seem to be mainly students at the Kaiserslautern Technical University who borrow a bike fur use during the semester. (Not intended for tourists, evidently.)
The other address was a bicycle shop called Fahrradhaus Kaufmann, Königstraße 37, Tel. 0631/21683.
I have since found an English-language website which lists lots of addresses, including this one, for bicycle rentals in Germany.
Also there is a (shorter) listing on the German Railways' website.
Second photo: Entrance to the Tourist Information. They have maps, books, souvenirs, tickets to local events, etc., but no bicycles.
As you can see from the photo, hundreds of people make use of the free roofed-over bicycle parking area at the main railroad station in Kaiserslautern.
This facility is not guarded, but there are hundreds of good racks for people to lock their bicycles to. Unlike a lot of other German cities, Kaiserslautern does not have a bicycle repair shop or rental service at the main station.
Second photo: For people with expensive bikes, there is also the option of renting one of these bicycle lockers.
Third photo: Here's the entrance to the bicycle parking facility.
For those diehards who are not concerned about their own health, public safety or the future of the planet, there is also a parking garage for automobiles on the other side of the tracks.
Kaiserslautern is still nearly four hundred kilometers from Paris, just as it always was, but the travel time is now greatly reduced since the French railway system opened a new high-speed stretch of tracks called TGV Est Europeen running more or less straight east from Paris.
The arrangement between the French and German railways is that the French TGV trains (meaning Train of Great Speed) use these tracks to connect Paris with Strasbourg, Karlsruhe and Stuttgart, with one train per day going all the way through to Munich.
The German InterCityExpress trains (ICE) use the same tracks but then veer off to the north to serve Saarbrücken, Kaiserslautern, Mannheim and Frankfurt am Main. Most of these ICE trains are non-stop between Saarbrücken and Paris, meaning that they don't stop on French territory at all until they get to the Paris East Station.
Second photo: An InterCityExpress (ICE) train in Kaiserslautern.
Third photo: The front of the main railway station in Kaiserslautern.