I don't think this sentence is correct. In French, to say someone has an eye color or a hair color is done via idiom. "Elle a aux yeux bleus," is correct. "Il a aux cheveux châtain." (He has brown [or chestnut] hair.) I am not a native speaker, but I have spoken the language well enough. Is anyone else familiar with this?
I am learning French but I think it is correct. See this link: http://www.linguee.fr/francais-anglais/search?source=auto&query=elle+a+les+yeux+bleus
It's not technically wrong, but it's a little misleading. It would require an unusual situation to make it reasonable. We don't use the article "the" in the ordinary way of things, when describing a person's eye colour, or hair colour. "Alice has blue eyes" is what we say.
We would only use the article to distinguish these particular eyes from some other ones, as has been mentioned in the comments above.
"The researchers split up the task of dissection. Dr. Jones has the brown eyes, Dr. Smith has the blue eyes."
"Each of our children had a one-in-four chance of being blue-eyed. In this family, it's Alice who has the blue eyes."
"I can't make dolls without eyes. Who has taken the blue eyes?"