I don't think we've routinely required ".com" to be part of the business branding of .com domain owners, but Ars Technica says he had that.
Does this mean they can seize the word “France” in other languages well?
So France didn't "seize" anything.
You can argue the govt of France shouldn't have filed this suit, but based on what reasoning? It's not really their job to protect the interests of US citizens. I mean, that's how it is. It's not very nice. In reverse, the US only seems to care about US citizens as well. I agree it would be nice if governments cared more about the rights of their allies' citizens as well, such as not violating their privacy on a global scale and not hacking into the private home computers of allies' citizens.
Also I kind of feel the article confuses the matter a little by referring to the guy as a "French-born American" (which isn't at all relevant enough to the case to lead with in the first paragraph), and incorrectly stating he "has now sued his home country" when he has in fact sued his country of birth. His home country is the USA if he's an American. (unless I got the meaning of those terms wrong, in which case I stand by the fact that it's confusing to lead with :) )
edit I think I wanted to reply to the sibling post, sorry for even more confusion :)