Booked everything in advance. No way I`d wanted to deal with finding a ride back to the airport on the spot while having to chaperone my group around (no one of whom spoke any French).
I have to agree that the tour Eiffel is a tourist trap and a ripoff. But it was worth it in this case. BTW, I`d not be surprised if you could book the combo ticket including the champagne for your children. Although the minimum drinking age in France is 16....