Thanks Mike,
You're right, that was not clear. Here are the actions, step by step, which led me to that:
-Creation of "Année 2008" directory
-Creation of all the directories into "Année 2008" (Bilan, Facture, Impots, Relevés, Payées, A Payer)
-Copy of "Année 2008" to Documents, the copied directory was then named "Copy of Année 2008"
-I renamed "Copy of Année 2008" to "Année 2009"
-I finally clicked the tree on the left and noticed the bug
I think it's a kind of refresh issue or something because when I tried to get to the Dashboard and then get back into the Document Library the problem was gone.