Find a cute little apartment in the 7th district, the left bank, or on the Ile la de cite. You can find one bedrooms for under 100 bucks per night.
See the Eiffel tower, the river seine, take the boat tour, walk the arc, see Notre dame and the Pont au Change (Napoleons bridge), the Louvre and the parliament building, go to some clubs and eat everything! be extremely careful, if you take the subway, it is not at all like the London version. I understand pickpockets will rob you almost as a matter of course.
So if you do use it, travel light, keep your phone in your hand and any valuables in a front buttoned pocket, not bag or money belt or purse. we decided that trying to keep an eye on your little brother it wouldn’t be worth it. as you guys are young and don’t have a little one, you probably could be very cautious and be okay.
The coffee isn’t so great, or at least not where I found it, the people are fabulous and the pastries are amazing, as is the high end food. eat out and at least one, maybe several nice restaurants.
You will always have Paris… but you might not get back…. so do it right!