We had a private tour with Desert Majesty (https://www.desertmajesty.com/tour-categories/day-trips/fes-day-trips/), a multi-day tour that started in Marrakech, but they can also arrange a custom guided daytrip from Fes. We’ve rented cars in a number of countries and done things on our own, but to get the most of our time in Morocco, I’m glad we used them. Send them an e-mail, and see what they could arrange, at what price.
While in Morocco, we encountered others who had a different tour company, and they reported that they were basically taken from one place after another that sold souvenirs, but Desert Majesty was not about taking us places for us to spend money. They are reputable and were well worth the cost of their tour.
One additional thought - are you staying at a riad
in Fes, and do they arrange for a daytrip tour? Do they suggest that a rental car is a worthwhile option?