Combining a suburban train service with the ability to navigate city streets sounds amazing. People can live nearer to the countryside, get frequent service into town, and, if everything lines up, commute straight into work without changes and avoiding the main station. The complementarity and opportunity to revitalise a branch line all sounds appealing... but a real challenge to implement. In France, only Mulhouse has truly achieved it.
Tram-trains aren't exactly rare in France: there are several lines around Paris, Nantes and Lyon have them (and many more had tram-train projects at some point). But, while the vehicles are capable of running in both modes, they are mostly used as a cheaper way to operate a line. The Nantes-Clisson and Nantes-Châteaubriant tram-trains, for example, which I have ridden, are just regional trains, running on heavy rail nearly all the way, and only stopping where the trains always used to.
Mulhouse is the only place in France to have true tram-train operations as described in the introduction: the tram-trains add traffic to line 3 between Mulhouse central station and Lutterbach, before switching to train mode and continuing on the branch line to Kruth as far as Thann.
The vehicles themselves are remarkable, as they need to be equipped for both streetcar and heavy rail operations, and each has its own requirements: lighting, horns, power supply, safety features... Mulhouse's vehicles are Siemens Avanto S70s, built in 2009-2010, and operated by SNCF as class U 25500. Similar units were introduced near Paris as early as 2005.