It suddenly occur to me she never has a relationship with anyone publicly, that is impossible in Hollywood! Then I try to google her boyfriend history and found NOTHING.
That is simply impossible, if she date with anyone, tabloids would catch them. The only answer to this is... lesbian?
Your problem is she doesn't live in the US, she lives in France so you need to stop looking for photos of her with men in People magazine or on TMZ. Look instead in French magazines like Paris Match. If you read the french rags you would find that she has had several long term relationships with men. Now no one has any sex tapes of her so just how straight she is is anyone's guess... but the reality is some women don't ever get married, it isn't a requirement for straight women to get married or even have kids, it's called a choice.
Just because she comes to the US for a couple of months of filming doesn't mean she lives here. Her home is in Paris which is where she spends most of her time. Even the list you've given has a lot more photos and articles in french media than you will find in the US.
Because she doesn't live in the US! Every single TV series or film she has been in the past 5 years was made outside of the US, mostly Europe... So if she only visits the US for the occasional TV appearance to push a film why would you expect her to be caught by US media. Just because she shows up on US TV doesn't mean she lives here.