Of course more is available, but the accommodation in the booklet is geared to budget (pilgrim) needs. All the information in the booklet is checked and updated each winter.
There will be many pilgrims on that stretch in September, but there is plenty of accommodation. Have a look at https://www.viefrancigene.org/en/accommodations-facilities/. Waymarking is good, and it would be difficult to get lost.
I would emphatically recommend the Lightfoot Guide by Paul Chinn. It gives route variants which can save time and energy over the 'official' route which zigzags all over the place in France.
They do not mean 'Easter week', which is the week following Easter Sunday. They mean Holy Week, which is from Palm Sunday to the end of the day before Easter Sunday. Holy Week in Spain sees many processions.
In Italian timbro; in French tampon. The stamps are more easy to come by in Italy, but the French are waking up to it as well. Also you can get one at the churches between Canterbury and Dover.
As @Bradypus says, the Confraternity of Pilgrims to Rome exists to give information and support to pilgrims wanting to walk or cycle to Rome. Their website provides a free planning pdf which can be downloaded https://pilgrimstorome.org.uk/planning/, and there is also an email information service...
Check this out. There is a whole section on cycling the VF (though mainly the northern part Canterbury to Rome) . There is also an accommodation list for the VF del Sud. https://pilgrimstorome.org.uk/planning/
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