Sort of depends which huts, but a few comments nonetheless:
The busiest huts are by far the Glacier Blanc and the Ecrins huts. That said, even there I’ve never booked before I’ve got a weather forecast - it’s not like the gouter!
For the others I’d typically have no qualms about ringing/going online a couple of days in advance.
That said, I’d probably think about booking a bit further out for a weekend slot.
It probably also depends on how wedded you are to any given objective. I’ve been pretty relaxed in the past and there’s so much on offer that there’s always something else good if on the off chance the chosen hut is full.
You’re also before the start of the busiest period which should help.
I’m sure Ecrins Collective will be along soon to give some more useful info but hopefully that’s some help in the meantime.
Sorry nothing else to add really , Tom sums it up very well.
I think his key point is, it depends on it you have set objectives such as the dome. If so then I would maybe drop them an email start of June, you could maybe make a provisional booking and then change it if the weather changes? But they would be able to advise on how late you could leave it.
we booked the Adele Planchard hut (for Grande Ruine) literally the day before, in July (2011). It turned out to be one of the best hut visits / summits we did. Quite full but the 9mile walk in (I think - brutal!) meant it wasn't rammed. Very cosy intimate hut, and a great 2-day trip with the Ruine summit in the bag & a LONG walk out ...... <ouch>
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