We originally had a trip scheduled to France for October and because I am immunocompromised, and Covid rates seem much lower in Spain, we are thinking of changing our trip to Spain for late October or early November. We would likely head to the south and would be looking at 2 1/2 weeks. Not at all averse to using a trip planning service, and limiting ourselves to 2 or 3 bases,but just wondering if it is too late to be trying to schedule a trip for this fall in terms of choice of accommodation etc. . We have not travelled outside of North America since 2019 and really have no idea how booked up places in Europe would be. We are in our mid sixties and somewhat “picky” about where we stay. Alternatively we can visit next Spring. So any planning we do now will not go to waste. Thankyou.

I wouldn't think so. I'm headed to Spain in late October and just recently made all my accommodation bookings. I'm now looking into trains, but can't book them yet as they're not yet available - I've not yet booked attractions, and will only book the really popular ones, which is on my to-do list for the coming weeks.

October and November should be fine in Spain. Last time we were there we booked a day ahead or at breakfast before we travelled for that evening.

It depends how picky you are. NB the star system in Europe is not the same as the star system in USA or even in different parts of Europe.

One possible issue is post Covid (Are we post yet?) some hotels have either closed or just cut back. I'd just start checking the usual sources. If you only need one room it's not going to take lottery winner luck but you never know.

I would start looking at a booking engine like Booking.com to see what is available and then at flights when you have worked out a rough itinerary. Quite often I make a provisional booking at a few hotels in places I like [with free cancellation of course] and then once my flights are booked I start looking in earnest. In 2 ½ weeks you could fly into Madrid, then get the train to Cordoba, [or rent a car] and tour the south from, say, Cordoba to Malaga, Granada, Ronda, and Seville with a few nights in Madrid at the end. You might like to look at the Paradors which may have some offers at that time of year. Or with just two of you you could just wing it.

Depending on your budget and itinerary, paradores can provide the accommodations you are looking for:

https://www.parador.es/en?gclid=Cj0K...B&gclsrc=aw.ds

I don't think it's too late for a late-autmn trip. I've made several trips to Spain, all in November or December, with (as I recall) no more than two months of prior plane and hotel bookings. But I wouldn't put it off too much longer. My most recent trip, though, was in 2019 (pre-Covid), and though I've been elsewhere since then, I don't have personal experience with the current situation in Spain.
I'm sure next spring would be a good time to travel, but recent health, economic, and climate conditions have all taught us how easily our travel plans can be blown away, so if this autumn is a good travel time for you, I would not suggest putting it off any longer.
I should point out that I usually travel solo, so I have enjoyed more flexibility than a couple or a group (whichever you are) would have. Also, while I've found late Nov. and early Dec. to be relatively tourist free, with hotel bookings easy, I seriously make a point of getting off the main tourist routes, so I don't know from experience what popular tourist destinations like Seville or Granada would be like in late autumn.

Of course it's not too late, I never book that far out. Well, pre-COvid days. A couple months is fine but I might not be as picky as you on hotels. I am somewhat, but mainly look for the location and moderate level. I think I often stay in a 4* in Spain but they were not as fancy as that might suggest.