Europe with the children will be unlike Europe when you were a backpacking college student or a young, married couple. But it will be still be a wonderful family trip, full of special moments, if you keep the children's needs foremost in your mind. You needn't shun cultural events or fancy restaurants, but you should pick and choose and time your outings carefully.
Teach the children basic European manners. Your child should be able to say a basic please, thank you and excuse me in the language of the country to which you are traveling. In many countries, English is a strong second language for many. But it's helpful to bridge any cultural divide and ameliorate any inadvertent etiquette errors by attempting some basic manners in the home language.
Focus activities on the child's schedule. Mornings are typically the best for most kids because they have the most energy and focus. Keep this time for cultural jaunts into the museum or exploration of the architecture or art that surrounds them. Leave afternoons for playing in the pool, going to the park or napping.
Research the museum program for kids. Many museums, such as the Louvre in Paris, have programs that are very accessible for kids (see Resources). They make the somewhat overwhelming or potentially boring very approachable and fun for your family.
Enjoy the absurd. When traveling with kids, things rarely go as planned. Couple that with being in a foreign country and the potential for irritation and annoyance abounds. However, rather than get frustrated, relish the opportunity to laugh and tell a story about the incident later.
Respect the culture. Rather than note how different things are, talk with your children about cultural customs they observe and the meaning or origin of the behavior. For example, Europeans eat differently than Americans do. Things as simple as holding a knife and fork differently, or eating late into the evening might be worth observing and discussing with your children.
Indulge, just once or twice, in McDonald's or Burger King. Your kids might enjoy the break, and you'll certainly be able to point out key differences, such as the use of the metric system in many European countries or the fact that you have to pay for ketchup packets in some European countries.