I would drive, esp. with kids and luggage for a long trip. I would break it up though, to at least three segments. Day 1: Frankfurt to Metz, and take a detour up the Rhine after you pass Mainz. Have lunch at one of the inns in the terraced vineyards. Metz has the new Pompidou Centre satellite, among other attractions. Day 2: Metz to Rheims. See the champagne vineyards and the greatest Gothic cathedrals. Day 3 Rheims to Paris. Each segment is just over 2 hours.
A GPS is obviously helpful, especially navigating in city centers.
n.b. I have driven in almost all countries in Western Europe, and I have done this very route. You get to see significantly more than on trains, not to mention the convenience of cars when traveling with kids or elderly. There are some cultural differences in highway driving, as others have noted, but I find them easy to adjust to. If you aren't comfortable with stick, upgrading to automatic is well worth the money, especially in urban or hilly situations.