Reasonable trip itinerary?

To be able to provide suggestions, what led you to choose these destinations? What about them appeals to you? They are somewhat far apart, but more significantly (to me), in each location (Carcassonne, Albi, Sarlat), there are so many other things to see and do, that it seems a bit of a shame that you won't have time.

The drive from Lyon to Albi via Carcassonne will be a long day; Google maps says 6 hours, and that doesn't include any stops for gas and other things. Add on to that a couple of hours in Carcassonne, and you're arriving in Albi late in the day. I have visited Albi, as a day trip. I thought it was nice, but I would visit only if I was already staying in that area.

In terms of the history of the region, Carcassonne is scenic, but some people don't like that it's heavily reconstructed. There are other (more ruinous) sites in the area that people find interesting and historic, but it depends on what you like. (Google "Cathar castles;" the terminology is not quite accurate, but will give you an idea of what I'm referring to - Lastours is close, and further southeast there's Queribus and Peyrepertuse). You could spend days in that area alone.

Sarlat and the entire Dordogne is worth many days, or a week. Do you like castles (primarily from the Hundred Years' War era), or prehistoric sites, or beautiful scenery and boat rides on a river, along with distinctive local cuisine? If you enjoy any of those, consider perhaps saving Albi and Carcassonne for another trip, and driving straight to the Dordogne.