To go to the Albert 1er hotel, you can take a taxi or the airport shuttle and get off at the "Jeanne d'Arc" stop which is the closest to the hotel (400 meters) There is a shuttle every 20 minutes from 5am to midnight. The ticket costs 9€.
If you pick up a car at the train station, walking there from the hotel is not a problem, it's a 15-minute walk and almost straight on 80% of the route. Take the avenue "Allée Jean-Jaures", it has wide sidewalks and a large central alley for pedestrians.
It is possible from Toulouse to go to Albi before going to St Cirq but you will have to leave Toulouse early because Toulouse → Albi is 50 minutes by the A68 motorway, plus the time spent in Albi, (parking, visit, etc) plus Albi → Saint Cirq almost 2 hours (only via small departmental roads)
Going directly from Toulouse to St Cirq will take you less than 2 hours via the A20 motorway.
So it's up to you, that being said Albi worth the detour. Even if you only stay there for 5 or 6 hours, you will have time to see the city and its cathedral.
If you still have some time left after leaving Albi, on the way to St Cirq you will pass Cordes sur Ciel which is also worth a visit.
https://www.la-toscane-occitane.com/en/towns-villages/cordes-sur-ciel