No one with the authority to do so (JK Rowling and her publishers) has officially given an age for Louis. In fact, we only know about him from some sketch Rowling did one day of the Weasley family tree.
Even if we can't get an age, however, we can get a relative figure; he's the youngest of Bill and Fleur's children, but Bill and Fleur were the first of the Weasley sibling to have offspring, so he might not be as young as, say, Lily. Objectively speaking, I would place him in the same Hogwarts year as Albus. I have however, read and written fanfics that take creative license with that.
By the way, Louis is also notable as the only officially announced male Veela in the series. While we don't know what that would mean in terms of his character, it'd probably play out in interesting ways.
Louis's eldest sister, Victoire, was born on 2 May 2000, the second anniversary of the victory over Voldemort and his forces. So his birthday could not be prior to 2003 at the earlest.