There's not a lot of activity in this forum so I don't check here very often so sorry for the delay in responding.
If you are talking about flat-towing your c-max, i.e. with all four wheels on the ground, there are two components involved. One is the baseplate and the second is the towbar. The two go together and usually have to be from the same company. The baseplate is permanently installed to the frame of the car and does require some cutting of the front fascia so the attachment points, lighting connector, and breakaway switch stick out from the front of the car. The towbar connects to those attachment points but is removable.
An individual towbar can be used with many different cars but the baseplate is custom made for the car chassis. In my case, for example, I got a Blue Ox Ascent towbar and a c-max-specific Blue Ox baseplate. If you're really handy and have the tools to remove and modify the front fascia of your car, you could possibly install the baseplate yourself and save some money. If you're not completely confident, I strongly recommend to take it to an experienced installer. Note that you also have to either have wiring run in the car for the tail/brake lights or use some magnetic lights.
For me, the towbar, baseplate, baseplate install, and wiring install was about $1,200 - not cheap. Of course if you already have a baseplate installed on your car, all you need is a compatible towbar. Again these two have to match - Blue Ox and Roadmaster are the biggest names in that market. I recommend you go to e-trailer.com where you can put in your car info and they will give you a list of compatible systems.
Also note if you plan to flat tow, in most US states you have to have a supplemental braking system in the car. Perhaps not in France but unless you have a really strong tow vehicle you'd not want to tow without a brake system.
Hope this helps.