French 'pop music' is continually criticised by UK visitors. After several years of exposure I tend to think of it as different, not better or worse. There are French groups and singers as capable as any UK / USA groups e.g. Kyo, Calogero, Pascal Obispo, Lara Fabian, Natasha St Pierre and others. See also French popstars.
International pop stars (US mainly) are also widely listened to along with a large number of French 'teen' stars.
The main difference in France is that there is often more focus on the tune and the words, with many 'well crafted' songs. These are often quite 'gentle' songs which lack the cutting edge appeal that a few UK or other groups may provide, but are none the less good songs.
The other main difference is that there is great reverence for good singing, and Charles Aznavour, Sacha Distel, Michel Sardou etc are loved by all.
In truth, pop music like many other things is now international, and much of what you hear in France is the same as you will hear elsewhere. The names of popstars from the US will be as well recognised by French youth as by UK youth.
On the other hand, there are very few modern French groups that are known outside the hexagon (France).
There are also singers like Johnny Halliday and Garou who are very popular for reasons I haven't yet fathomed. And as for Florent Pagny singing 'baritone' - now THAT is bad!
Try to listen to it in the car instead of your Avril Lavigne tape, you might be surprised.