People often forget that people in different time periods had different concepts of what race and racism were, and the concept of racism itself is honestly a fairly recent concept as an ideology in general. Bridgitte Bardot was from a different time and, while the comments may have been racist, she may not have considered them as such.
Inciting racial hatred which leads to violence is almost like sedition or yelling "fire" in a crowded room. You simply can't do that. Yes, America has free speech. But knowingly saying something that can cause violence should be illegal. We can't say things like "kill the president" without getting in trouble, so Brigitte Bardot's fine was perfectly fair. At least she wasn't jailed.
Of course it was fair for Bridgitte Bardot to be fined for inciting racial hatred. Have you kept up with this woman since her 15 minutes of fame a half century ago? She's insane. And she's also a pretty noted bigot. Private companies have the right to fire bigots if they want.
I believe the French government has the right to fine their citizens as they see fit based on their actions. She obviously wasn't falsely accused because the racial hatred was clearly published in her book. Personally, I think these fines are appropriate, maybe the United States should adopt similar laws.
I think that it is extremely silly for the woman to be fined for inciting racial hatred when governments all over Europe are making the lives of conservative Muslims difficult, either with certain clothing bans or refusals to separate swimming classes. I also think that it is the height of insanity to charge somebody with inciting racial hatred when, the last time that I checked, Muslim is not a race.