Our agent immobilier recommended Verisure, which apparently is very popular in the area. (She uses the video feature to keep an eye on her cat while during the day.) If someone breaks in they have round-the-clock monitors and will alert the police, along with other optional bells and whistles. We like our system very much, although having just bought the house no break-ins yet.
Of course you pay for this, so you have to weigh the costs and benefits. Also our experience was they have very hard-sell sales tactics compared with other French services we’ve dealt with so far. When we contacted them they set up the appointment and installed the system very quickly. Fortunately we’d done our research and knew exactly what we wanted, so it worked well in our case, but I would review the website offerings carefully before reaching out.