Hi Chris,
I've walked the Le Puy route twice, once in 1996 and again in 2005, both times in one go, leaving Le Puy towards the end of April. The route is tough but beautiful and as you leave Le Puy you climb on to the Aubrac Plateau where you are very exposed and the weather conditions can be very wet, with visibility down to 30 metres at times. You will descend 1st or 2nd day into St. Privat d'Allier - in wet weather the descent can be quite dangerous under foot - I got away with some stitches in my face but I heard that others had broken bones.
I found the gites comfortable; those that are run locally have to have both showers and cooking facilities and therefore needn't be too expensive. There is also plenty of private accommodation.
Regarding numbers there are some things to be considered. Firstly, there are about 50 pilgrims a day leaving Le Puy in the final days of April, this rises to about 200 per day at the height of summer; so on that count you should be ok for accommodation. Secondly, as you move along the route numbers may build as pilgrims who have walked for a week or two in previous years pick up their pilgrimage again. Then there is the third factor, the route is popular with walkers and so numbers may also increase at weekends or around the time of feast days, eg Pentecost; once or twice had to go off route for a bed.
You will probably be one of the exceptions on this route in that you intend to walk all the way, I found most pilgrims could only spare the time to walk for about 2 weeks. There were one or two others walking all the way but they but they were going at a different pace from me, but I eventually finished walking with 2 pilgrims who had started again at Cahors and Moissac and we arrived in Santiago the same day.
It is different from the route in Spain in that there are fewer pilgrims and certainly far less than in Spain in summer. With fewer mumbers the atmosphere can be calmer, more relaxed, less stressful.
That's all for the moment but if you have a questions, feel free.
Best wishes,
Brendan