If you are talking about speaking French as a first language, this is false, except possibly in relation to the upper reaches of the aristocracy. If you are talking about speaking French as a second language, then this continued to be a marker of class for a long time afterwards.

In a highly class-conscious society where the vast majority of people spoke English as their first language, it seems fairly unlikely that accent would have had no connotation of social status.

It thus seems hard to believe that the development of the modern diversity of English dialects would have been spurred by some sudden need to mark class distinctions.