Search October in the search box and you'll see many positive comments about walking then. I (68-year-solo-female) have walked 3 times in Oct-Nov, and I think it is a great time to walk; perhaps the best for the
Camino Frances. This year I have conflicts in the fall, and I want to do the VdlP, so I'm switching to the spring.
You should go prepared for all types of weather from hot and sunny to cold, windy, rainy or even snow. That means a sleeping bag, several thin layers rather than any thick ones, good rain gear, hat or buff, and light gloves. Still, my pack weighed only 6-6.5 kg without water.
There are plenty of people walking, so you will have the opportunity to walk with or within sight of others, but you can be alone if you want. In mid to late October, I think that about 100 people stay at the albergue in Roncesvalles each night. How many people do you need?
I think the numbers are about perfect- enough for company if you want, and not so many that you can't get away from others.
If you are concerned about being too alone on the trail, stay at the popular albergues and get on the road at first light (8 a.m.) with everyone else. I often stayed in private accommodation, and took my lazy time in the mornings, so I was behind most other people.
In mid-October, some albergues close for the winter. There is still enough accommodation within reasonable distances, but you should be aware that some small villages might not have places open. Just look at the route ahead for the day and talk to other people about the options.
Go ahead and do it this fall! Buen camino!