The Disney hotels are at top pricing for Christmas week, so I think that's pretty telling how busy it is. Here are a couple of crowd calendars. First one is in Japanese, decipherable using google translate.
http://www15.plala.or.jp/gcap/disney/
http://tdrnavi.jp/forecast/disneyland?lang=en
We're tied to the school calendar as well. We went in early June as soon as the kids got out of school. The Disney hotels on weekdays were value pricing. The crowd level on the weekdays felt okay. We went to Tokyo Disneyland on a Sunday and it was definitely more crowded but still manageable. Thinking back to when we went to WDW in early April before Easter (which was late that year), I think WDW felt more crowded.
One of the nice things about TDR is that the Japanese people are very polite and orderly. For parades, everyone sits except the people at the very back, so we just sat down about 15 minutes before several rows back and didn't have a problem seeing.
The weather was humid and a bit hot if the sun was out, think temperature was about 80 degrees F. Not bad at all and this is coming from a spoiled Californian weather wise.
Not sure when your kids get out of school, but I would be more worried with late June since that's when the rainy season starts.
As for the language barriers, it wasn't that big of a deal. In tourist areas, if the employee can't understand you, they can usually find someone who can. Or for simple things, they remember a few English words along with hand gestures, it works out. I basically got along with only arigato (thank you - though arigatou gozaimasu would be more polite) and sumimasen (sorry/excuse me).
Most restaurant have pictures in the menus you can point to. The menus at TDR have English. At counter service restaurants, if the menu is on a board, the CM will pull out a menu you can point to if they're not sure they understood you correctly or if they want to ask you about an option for the meal sets.
Good luck deciding Japan or France, I don't think you can go wrong either way.