You asked about other countries. Have you considered the Baltic Coast, paarticularly Gdansk and Sopot in Poland? Summer temperatures will be warm but not stifling, prices are reasonable (except the big Western giants all who have a presence there, Marriott, Hilton, Radisson, Sofitel et al and if they're there then you know that it's far from a less desirable destination). You can have a mix of history, culture and beach time.
Or there's the UK, the Northeastern Coast, East Anglia, the South Coast, Devon, Dorset and Cornwall, Wales, the Lake District etc. A wealth of activities to interest and occupy everyone and late July/August will usually be good weather and unlikely to be on a par with much of continental Europe.
Ok, you won't have the Louvre, Marienplatz or Anne Frank's house but you also won't have the queues and are the kids really going to be interested in any of that anyway?
Travelling to Europe with young children from somewhere like the US is tricky. The desire and temptation to see as much of the famous sights as possible,to experience as many countries and cultures as possible is understandable but you have to be realistic. We've found over the years that the best holidays have been those were we weren't rushing here, there and everywhere, trying to cram everything in. We didn't even go anywhere near the Eiffel Tower when in Paris, we saw it from a distance whilst having an excellent lunch, did it diminish our memory of it because we didn't climb it? No, in fact our experience was probably better, no waiting in line for hours, climbing the steps or squeezing into elevators. We had a perfect view of an icon, an excellent panorama of the city and a very good, enjoyable meal whilst taking it all in. Do I have any desire to return to Paris and climb the tower? No.
Besides, can there be anything more miserable than a major city's public transport in the middle of summer? The Tube, Paris' Metro, Rome's Metro? And with two young kids!!!
A multi stop route along France's coast, either the one flanked by the Bay of Biscay or the more northerly Brittany area would provide ample experience of a foreign country and dependant on route you can also dip into Spain or the Channel Islands or British mainland. Being on the coast provides a cooler experience during a heatwave (believe me, living on top of a hill less than a mile from the sea on the south coast of England makes a huge difference to temperature and comfort during hot weather) and renting cottages, villas etc along the way makes life with young children far easier. You don't need to introduce them to five or six different countries at that age, it mostly goes over their head and they'll often not remember what you hoped they'd remember.
You're young (I presume), your kids are young, assume you'll be back. We've been visiting the US every year for the last ten years ever since our youngest was two. With the exception of NYC when our youngest was three, none of those visits involved substantive time in cities (our youngest recalls very little about NYC other than FAO Schwarz with a giant Elmo, a Spongebob Squarepants icecream and the penguins at the zoo). Both of them have very strong memories about various theme parks, water parks, amazing pools and beaches but ask them about lunch at the oldest building in Savannah, GA and you'll receive a blank stare. The Liberty Bell in Philadelphia? No idea! Jamestown, VA? Nothing but ask them about the Spy Museum in Washington DC and they'll recall a huge amount of detail likewise the airboat ride through the Everglades and many other activities that wouldn't be the obvious choice in a major tourist destination.
