End of August in France

It depends what you mean by "overly crowded." The Loire region is a popular tourist destination, but it's spread out so you will not be up against hordes like what's typical at Versailles or the Eiffel Tower. Plus, as you mentioned, many Americans will have gone home because our schools are starting up by then.

And many other older Americans and Europeans will be traveling because those with children are out of the way. September in Europe is a prime travel month. Overly crowded is relative.

September in Paris is particularly crowded because of conventions and shows. That won't spill over into the Loire, but may affect your time in Paris.

Euros (or actually the plural is the singular Euro) is the money that some Europeans use - not the people themselves. So the Euros will only be on holiday if the people who own them take them with them. The ones that have to stay in the bank don't get a holiday - they just have to stay cooped up in the bank vault with lots of their other Euro friends. Just by the way...

The old concept that all of France takes the month of August off and that all businesses close for the month may have been true to some degree in the not recent past but that is not necessarily true now. I've never had any problems in August.

We’ve actually traveled to France in late August/September twice and really enjoyed it. The places we’ve been seem to stagger their vacation schedules so that not everything is closed at once. We never had a problems with things being more crowded than any other time; major Paris attractions are always crowded. I would say that arriving close to the opening time or later in the afternoon probably gives you the best option for avoiding crowds at museums and chateaux.