However, you must be well-organised and prepared for compromises. Here is a list of what our children love to do and what we are happy to trot along with - in good weather and bad - always trying to keep costs down.
If it's sunny, I suggest you go immediately to the Eiffel tower. The problem is the queues: the round-trip to the top can take three hours. Do you really want to go up, when pollution and smog obscure the view? No child I know has ever asked to go to the top a second time. It's tricky, but if you can manage to persuade your children to go for a boat ride on the Seine when they have had their photograph taken below the Eiffel tower, I think you will have engineered the right decision (cost 20F to 57F, depending on how high you go).
For the boat trip, you can walk to the bateaux-mouches at the Pont d'Alma, passing by the flame above the underpass where the most famous car accident in history took place and glancing at the bizarre and touching messages left there for Princess Diana and Dodi Fayed. You can catch up on the latest conspiracy theories carved into the wall, as the City of Paris hasn't decided what to do with this makeshift shrine (originally a gift to the city from US citizens).
The boat trip is fun. It goes around the le de la Cite, so you get an excellent view of Notre Dame. At 40F for an adult and 20F per child, it is good value. There are no refreshments on board, so first pop into a bakery for patisseries and a supermarket for drinks.
After the boat trip, try walking up the avenue Marceau to the Arc de Triomphe - again, you may have difficulty avoiding going up to the top, but at least the queues aren't bad (35F). Back along the Champs Elysees to the Tuileries gardens, with its small playground and cafe. Go a little farther and you can take in the Pyramid at the Louvre. (The Louvre itself is a bit ambitious if you're on a tight schedule.)
Now reward the children by taking them to the fabulous enclosed playground in the Luxembourg Gardens. It galls me to pay 13F per child and infuriates me that I have to pay 7F to watch them, but with my cup of delicious coffee from the food stall nearby, and the best loos in Paris for 2.50F per person, I enjoy my people-watching time there.
When I ask friends where they take their children for an evening meal in Paris, there is always an embarrassed admission that the place that works best is Hippopotamus. This chain does good food for children (menu, plus drink, balloon, colouring pencils and booklet, is 50F) and reasonable food for the oldies. Two other chains worth trying are Chez Leon and Bistro Romain. Unfortunately, though, Paris is not Italy; only extremely well- behaved children are welcome in restaurants. It is only outside Paris that you see children out with the family enjoying their food.
But what if it's raining? Paris seems to have its own particular type. There are no quick showers - it rains heavily for days. Last May and June were particularly bad, so be prepared.
I would suggest a first stop at the Musee d'Orsay. Children are a positive advantage here, as a lady patrols the queue plucking out worthy families to be brought to the head of it. And in one of the most civilised gestures towards families anywhere, there is no entry charge for those under 18 (adults 40F).
The building itself, a converted railway station, is a treat. The Impressionist art does seem a bit squashed, but Degas's ballet dancers are always a hit with little girls. And if you have seen Bean: The Ultimate Disaster Movie, you can play a game of finding the painting of Whistler's mother. A snack at the cafe behind the clock is worthwhile.
My children enjoyed the Magic museum in the Marais (11 Rue St Paul, Metro St Paul, 45F per adult, 30F per child) but I found it disappointing. The Picasso museum, on the other hand, was a delight (rue Thorigny, Metro St Paul, adults 40F, children 30F). Visitors wander through a refurbished merchant's house seeing how the artist's style developed over the years.
The home of Victor Hugo (entrance 17F) in the stunning place des Vosges is also small enough not to be thought "boring". For older children, try the fascinating catacombs (under Metro Denfert-Rochereau) and the wax museum (Musee Grevin, blvd Montmartre, Metro Rue Montmartre).
Parisians love puppet shows, and although in French, the stories are easy to follow and audience participation is encouraged. The Luxembourg Gardens theatre is covered, so you can escape the rain for about 50 minutes (23F per person, two shows every afternoon, except school days).
There are lots of other activities (The Science Museum at La Villette and Aquaboulevard, a giant hi-tech swimming-pool complex) but frequently they are in the less picturesque parts of Paris, which I don't think are worth the detour if you are in the city for a short break. The boat trip can also be done in the rain because it is covered.
Eurostar (0345 303030) has a special carriage for families, with tables for picnics and games. Baby-changing facilities are excellent. Use the lift at Waterloo; it's awkward on the escalators with children and buggies. In Paris, cheerful men help you on to the train. At Waterloo there is a pounds 5 charge for this. Buy a carnet of Metro tickets at Waterloo; queues are long in Paris.