I'm not an expat in France, I'm actually a French expat living in Melbourne, so my experiences might be a bit different (also your post is a month old so I don't know if you'll see this message), but I thought I'd chip in anyway
As the person above said, September or late August is indeed the ideal time to move since it's the start of the new school year, but it doesn't mean you won't be able to enrol your kids in clubs. Not-school-related clubs are definitely a very good idea, because schools tend to focus only on formal education and don't usually offer a lot of other options. Crafts, music, sports, etc are done separately on whatever day the kids don't have school. It's a good chance for the kids to bond with other children, and a chance for you to hang out with the parents.
And I also second the "cantine" (school restaurant) thing. The vast majority of the kids do stay there for lunch and it's a great chance for social interactions. The lunch break is usually quite long and the kids are expected to stay at the table until everyone is done, so that will give them plenty of time to chat. Also the food is healthy, if not always as tasty as the kids would like
I guess the 2 main differences between Lyon and Toulouse are:
- How cold do you like your winters to be (it gets much colder in Lyon)?
- Do you like skiing and hiking better than swimming at the beach?
Not that Toulouse is actually close to the sea, but you can get to the Mediterranean sea by train very easily. The Pyrenees are also very close and you can drive to Spain. From Lyon you can take full advantage of the Alps, and you can take easy road trips to Switzerland and Italy.
It might sound a bit silly, but I think a good way to fit in in France is to follow the locals' approach to food. The time spent at the table is generally longer than in Australia and everyone eats at the same time (as in, no random snacking at 5:30 which results in the classic "I'm not hungry" when it's time for dinner). People generally bond over food and drinks, and I think the first step in making friends is inviting people (neighbours, other parents, etc.) over for the "apero". You might already know what it is, but just in case, it's the drinks people have before a meal (usually before dinner, but it can be before lunch as well). People would come over around 6pm and you'd all have a drink and a few bite size snacks while the kids play. When it gets around 7-7:30 you might offer them to stay for dinner (if it's the 1st time you invite each other over, they might say no, to be polite, but they'll probably say yes next time). And next time they'll invite you guys!
Keep in mind that most people do speak English, they're just embarrassed because their accent is really strong, and they probably haven't had a chance to speak it since they were at school. I've heard many times that French people refused to speak (or learn) English out of pride, but honestly, I think it has more to do with not wanting to sound stupid. Oral English isn't taught in a good way in France and we end up feeling ashamed to even try, right from the start of the learning process. If at first you use a mix of languages, with a little bit of French and quite a bit of English, it should work. People know the words and the basic grammar. They're just being shy
Also, unfortunately, because most French people don't have a positive experience with language learning, and are not familiar with the struggle of trying to speak because you absolutely have to, they tend to correct foreigners' French a lot. I know, it's really annoying and it can be a bit discouraging. Please don't take offense at this, and don't think it's because your French is awful. They've basically been told "if you can't speak a foreign language perfectly, don't even try because you sound ridiculous". Some people are not familiar with the long and gradual learning process of languages, because they've been taught badly. They're trying to help, just not in a way that's actually helpful.
And if you end up settling in Toulouse, another good way to bond is to like (or pretend to like) rugby
So yeah. These are of course not experiences from an expat point of view, so I don't know how useful it is, but if you've got questions and no one to answer them, feel free to ask