There are a variety of routes mainly as covered above:
The one you've indicated, via Paris. This can also be done as an overnight sleeper Paris to St Gervais depending on the day of the week. Then Chamonix valley train from St Gervais to Les Houches OR just start your walk from St Gervais - no particular reason to commence at Les Houches.
Eurostar to Geneva (change at Lille, just walk from one platform to another), then either local train or transfer bus from GVA. Bear in mind the local train is very slow and requires 3 changes; I think its easier to go GVA to Champex instead, or get yourself to GVA airport and pick up the alpybus or easybus from there.
a) you can fly very cheaply to GVA then get a transfer bus (e.g. easybus or alpybus) to Les Houches.
b) you could look at starting in Champex which is reachable via bus from Orsieres, that in turn is on the Swiss rail network, 2h from Geneva or various other places.
That may leave you more, rather than less, boggled.
Tour de ruan worth looking at for something a bit different near Chamonix - in a much less popular part of the mountains there. Chamonix wild camping rules are that you can put up a tent at dusk and take it down at dawn (technically, "bivouacing"; camping during the day is illegal in much of the massif). If near a mountain hut, ask the guardian's permission - it's rarely refused, and they will often tell you the best places.
I try and have a good understanding of what's coming up - either from the map or reccying the walk first. e.g. 'in about 15 minutes we'll get to a really nice stream to throw rocks in' or 'there's a steep climb ahead so we'll stop at the top for a snack'. My kids seem to cope much better by breaking the trip into lots of small parts and just focussing on the next goal.
My son (then 7) did a 42 mile/8 day backpacking trip last summer, and both my kids (son now 8, daughter 5) are coming on a 8 day/30 miler this summer.
I never ever carry mine, I don't want them to learn/think that is an option, as when backpacking it isn't. Instead we just have breaks and make sure we always leave a lot of spare time in the planning.
For occasional usage (i.e. the c. 4months/year that I actually need one) the inreach works out cheaper and has vastly greater functionality - email, text, weather reports etc. The spot feels like obsolete technology with its absence of 2-way comms.