I've thought about this a bit because it was debated a lot even when I lived in France 9 years ago.
First, it just strikes me as SO French. My personal experience was that France is a very homogeneous country in that people there believe it's appropriate to decide (through lots of open debate) what it really means to be French. Once it's been decided, it's acceptable to expect everyone in the country to follow that definition of French-ness. In the US there is much more of a tradition of regional variations and local control, and those differences are celebrated. For example, there is a national school curriculum in France and that would definitely not fly in the US.
Second, I think that anti-veil/burka clothing legislation is racist. There are nuns who wear full habits - their faces aren't covered, but much more of their body is covered by a habit than by if they wore a traditional veil. I can't imagine anyone trying to outlaw the clothing of white European nuns.
Third, I think that wearing a burka or being in a society where many women wear one would be incredibly interesting. I've wanted to try it for a long time. It's a bit like a school uniform, in that it takes away all of your choice and therefore also your worry about what to wear. There are some women who find it liberating to be in public but also hidden in their appearance. I can see the appeal of this, especially in societies where women are considered at fault if they experience sexual assault. Being hidden, and therefore less exposed to the male gaze, would have its benefits. I don't think it's appropriate to tell those women that their choices are invalid or illegal.
Fourth, I think that any legislation of what people wear is wrong. Probably this reflects my American tendency to shout FREEDOM! but I do think people should have autonomy over their bodies, including how they dress. Dress codes for school or work are different because people who dislike them can (theoretically) choose other schools or workplaces. But legislation? I just think it's too much.
Fifth, I think that treating anyone badly because of what s/he wears is wrong. All people deserve respectful treatment, whether it's a man in an expensive suit, a woman in a burka, or someone wearing a burlap sack or a giant duck suit.