I definitely recommend taking the Eurostar train from London to Paris. The transport links are so easy (city center to city center). There’s great leg room (I bought my tickets the first day they were available, so I was able to snag one of the table seats for the three of us. Oh, and the further out you buy your tickets, the cheaper they are). So we left our hotel at about 11:00, grabbed lunch for the train at St. Pancras, and were in Paris by 3:00 (and did I mention there’s an hour time change in the middle).
Our first day, we just wandered around. Started at the Eiffel Tower (which sadly was just closing as we arrived – Sunday hours). So we wandered around the Seine instead, which was really amazing. I’ve seen plenty of pictures, and scenes from tv shows, and it was just so cool to actually be there.