Your stages look good to me. I’ve walked longer stages from Le Puy, but next time (probably later this year) i expect i’ll walk the same as you or very similar. Sauvage is very popular so be prepared to book elsewhere. Ferme du Barry also, but there other good options in town. There are also good options before Nasbinals so you could make the day a bit shorter.
Yes May is busy. You may well be ok not booking, but it’s probably prudent to do so.
I’ve walked on the via Podiensis a few times in September which is also a busy month. I book the first 3 days, then book ahead for 2 or 3 days normally. But if i was walking in May i think i’d try book them all ahead.
You don’t need to speak French, i don’t and have managed just fine, with bookings and with communal meals.
Most places have email addresses. I booked most of mine that way last year. i used Google translate. And included the French (top of email) and English so the hosts would get that i’m an English speaker.
When i rang places to stay i’d have my request written down in French.
Hello, do you have a bed for this evening (or tomorrow evening). With demi pension.
My name is …
My phone number is …
I have found that quite a few hosts speak enough English to at least take a booking.
And often if i try speaking French they realise that i’m an English speaker and start talking in English to help me