Kelly, you can get by without one. I walked the Le Puy route without one, but there are reasons why I would probably take one next time. People do tend to reserve ahead on the Le Puy route, and often, though not always, just the day before is enough. You will always find a bed, but depending on when you walk, you may miss out on the cheaper ones if you haven't booked, and end up spending more on a chambre d'hote (like a b&b) or hotel.
There are two main reasons I would probably take a cell phone next time. The first is simply that French chip phone cards don't seem to work in all French pay phones, and more than once I arrived in villages where I couldn't use the pay phone. Sometimes the owner of the place I was staying in would ring up and reserve ahead for me, but sometimes I had to wait until I reached a village with a compatible phone booth.
The second reason is that quite often you just got an answerphone when you tried to reserve, and they asked for a number so they could ring you back. Without a mobile, you could only leave a message about the day you wanted, without getting any confirmation.
A third, but less important reason, is that sometimes people wanted a cell phone number so they could ring you and check if you were still coming, in case they had people waiting hoping for a bed, and you hadn't arrived. However, as an English speaker, it seemed they weren't too worried I couldn't give them a cell number.
A fourth occasional reason is that sometimes you walk past advertising boards with a phone number for a gite/chambre d'hote that might be a bit off the GR. If you ring the number provided, the people will come and collect you then drop you back on the GR in the morning.
I met a South African woman walking who didn't speak any French. She found that with her Miam Miam Dodo guide she could pick out where she might want to stay next, and then she would always find a willing French-speaking pilgrim who would use her cell phone to make a reservation on her behalf.
Phew, I have been very long-winded here!!! Whether you decide to take one or not, I am sure you will enjoy your Chemin!
Margaret