In France, the growth in individual car ownership is continuing to slow and the number of individual cars on the road has levelled off since the 2000s, especially in more urban areas. How do these phenomena fit in with the long-term spread of cars from the well-to-do classes to the more modest population categories? We describe this process from 1974 to 2010 for Metropolitan France and for Greater Paris, making a distinction between households according to their positions in the standards of living quartiles. On the national scale the hypothesis that well-off households, the middle classes and more modest households have ownership and use trajectories that converge towards the same automobile ceiling was not invalidated. To evaluate this ceiling we adjusted Chapman-Richards sigmoid curves to automobile ownership and use series. More flexible and better suited to our context than standard logistic functions, they put this ceiling around 0.76 car per adult, and 16,200 kilometres per year per household if fuel prices were to be maintained at their 2010 level. This distance-travelled ceiling is modulated by an elasticity of -0.24, reflecting reactions to erratic fuel price movements. In Greater Paris, however, the distances travelled peaked earliest for the wealthiest households, before the rise in fuel prices of the 2000s, suggesting the onset of a major trend of which residents of Île-de-France were precursors.