j4, it appears that you already have your long-distance train tickets (you left out your home country in your profile). But it might have been better to take the Eurostar (? you didn't say) all the way to Brussels, which is an easy single train to Bruges. I guess also that you prefer to rent the car in the same country where you are returning it, to save drop off fees.
I happen to like art museums, so I spent a whole day at the important and famous Palais de Beaux Arts in Lille. But because Brugge is so accessible from Belgium (as opposed to France) I would consider instead (maybe even getting the car sooner) and visiting Louvre Lens. I'd also observe that while it is not right next to Lille, Gent is easier to get to, and is at least 60% as nice as Brugge.
I trust you know that the two major rail stations in Lille, while not side-by-side, are connected by a passageway.