Eurostar really is a great service and avoids all that messing about getting to LHR or LGW (depending upon where you are staying) and ditto for the other end. Trains really do go to the heart of a city. By the time you went from St Pancras to LHR, checked in, waited, security etc etc you'd probably already be in Paris on the Eurostar (2 1/2 hours).

I'm not sure of your interests but check out the new Notre Dame Cathedral. It's not hard to spend a day just in Île de la Cité. Lunch at La Tour d'Argent. Take a day tour to Reims (Champagne).

From Amsterdam or Brussels there are day tours to Bruges and Ghent. Personally I'm not a big fan of Brussels itself.

From Lille or Brussels it's not hard to reach the Word War 1 sites of Belgium and Northern France. They are incredibly moving.

I think I'd keep it simple and head to Paris and focus on just a few neighbourhoods.