Contrary to what you'll often hear, I think Luxembourg is a beautiful little country, well worth visiting on a European trip when you are in the neighborhood AND if you have some time. The capital is nice but doesn't compare (at all) to the great cities of Europe in terms of monuments and 5-star attractions. There are other places in Luxembourg that are under-rated and not famous (and not crawling with foreign tourists) that I really liked. That said, I don't think Luxembourg fits with your other criteria.
You need to limit your ambitions -- take it from me, I usualy try to do too much on a trip.
I'd reiterate my suggestion above: spend your week in France, focus on Paris with probably one (or MAYBE two) French side-trips (only two if you're willing to shave off a couple days from Paris). Pick one side-trip: either the Loire Valley chateaux or Normandy/Mont St. Michel. Jump on the train and go spend a day or two each in Bruges and Amsterdam.
The timing of the sequence depends on where your flights go. Ideally, you could fly in to Paris and out of Amsterdam (or vice versa), that way you don't have to double-back to Paris.
I'd fly in to Paris, spend the bettre part of a week there, then do your side-trip (Normandy or Loire; consider renting a car for part of that), then catch a train to Bruges (probably via Brussels, so you can spend a few hours there on the way), do 2 days in Bruges, then train to Amsterdam for your last 2 days, fly home from there.
That would give you a nice diverse trip, focused on several of the major cities, but with a little of the countryside and a nice slice of different countries/cultures.