There are 6 classes of certificates. The air quality certificate helps to favor the least polluting vehicles:
Favorable parking arrangements;
Preferred traffic conditions;
In restricted traffic areas (ZCR) or in the event of a pollution peak.
The air quality certificate is mandatory to circulate in the restricted zones established by certain local authorities (Paris) or to circulate when the prefect introduces the differentiated traffic during certain episodes of pollution.
Above are 2 official examples of 'Crit'Air' stickers in place on car windscreens.
On the LEFT as class 3 is a 2008 2.7 Turbo Diesel engined car, on the RIGHT in class 1 is a 2017 1.4 Turbo Petrol engined car (both images have had some detail removed for security.)
The actual class will determine where a car can go depending on the restrictions applied in any particular area. central Paris and Lyon are the only places you may be stopped entering in anything under class 1, but that can and will change in the future.