Richard, congratulations on your decision to walk
Camino Frances. We've walked the CF three times in mid-Sept to late October and are planning our fourth this fall, same time. The weather varies a bit. Some days can be warm, but not brutally hot. Some mornings can be cool, but not bitter cold. Most days start in the 40s and the temps can climb to the low to mid 70s. We've had clear days each time climbing to Roncesvalles, but for some reason, we've had rain the last two caminos on the hike to Zubiri. The last two years we've had clear days with blue skies for several weeks. When entering Galicia, it's not unusual to get rain for one or several days.
With regards to your hiking plan, covering 800 kms in 28 stages is ambitious.
Brierley's guidebook suggests 35 days, including two rest days. Our first camino, we hiked 34 days and had one rest day, the second one with my brother and his wife, we had 36 days and 2 rest days, and last fall we had 37 hiking days, no rest days. This fall, we're planning 35 hiking days, no rest days.
As Trecile commented, the early stages for
Camino Frances includes lots of pilgrim traffic. We made advance reservations for caminos two, three and our upcoming one for every night of the camino. I suggest you book reservations for St Jean, Zubiri, and Pamplona. You can monitor traffic and decide whether or not to book more reservations. Gronze and Booking.com are great resources.
Buen camino !
Bob