I think these forums are the greatest contact I have with native French. I myself am an American with European roots a few generations removed.
My sister-in-law and her husband have emmigrated to France and just gave birth to their first child. They are ethnically and racially Chinese. I was kind of surprised when they decided not to give their new born daughter a French name, but only use the Chinese name which they picked for her.
In my mind, not having a French name will present a small obstacle for the child to assimilate into French society. (Of course, it is possible that her parents are not that eager for their child to assimilate.) Additionally, the child's Chinese name gives no indication as to the gender of the child. (This is true even for Chinese speakers as the name chosen is fairly neuter.)
My sister-in-law explained it to my wife that in France that the native French do not expect or appreciate assimilation by non-ethnic/non-white persons. They are generally uncomfortable using French names for people who they regard as foreigners and prefer to use a foreign sounding names to address such people. In general, being born ethnically non-French and racially non-white will make you an outsider to French society regardless of any desire to assimilate.
Of course, my comments above and my sister-in-law's view are very broad generalizations. However, a society is really composed of a multitude of distinct views. In any case, I would be interested to hear the thoughts of those who are ethnically and racially French.
In the USA, someone born here can certainly assimilate if one desires to do so. That is not to say that racial and ethnic prejudices don't exist here. However, they are not so broad or extreme across the entire society to exclude someone from being considered an American in most venues if that is what the individual desires.
Thanks for your time.