Is Nana selfish?
She leaves her family for...what exactly? She claims to have big dreams but has no idea how to fulfill them, and seems unmotivated to find out. Although we are told she is "forced" into prostitution by her financial circumstances, once she settles into what the French call "the Life", she seems perfectly content with it. How much further effort does she make to better her life and achieve what she claims are her goals? And even after all this, going back to her family is completely out of the question for her. Yes, I realize there are instances where someone's home life is so toxic or abusive, they have to get out. But Godard seems to be implying that isn't the case here. Nana gives the impression she left simply because she was bored. I think we can agree that abandoning a spouse is a far different thing than abandoning a child. What makes her new life so preferable to the one she left behind?
As Ebert points out, there's a lot about Nana we don't know. Somehow, I think even knowing her back story wouldn't make her character any more likable. But then, Godard was never concerned with making likable characters, was he? As an American raised mostly on Hollywood films, it's hard to just go into observation mode and not try to determine whether the people on the screen are good or bad, right or wrong, likable or detestable. In French New Wave cinema, it's all a moot question. It neither condones nor condemns. The characters are meant to be observed, not judged, even if their actions are not justifiable. Likewise, Godard seems to be using the character of Nana to prove no point at all.
And maybe that is the point.
"Farts! Double farts! Turds! Double Turds!"
--Caddyshack, 1980