Can anyone let me know the best way to travel from Sarlat to Saint-Antonin-Noble-Val
The best way is undoubtedly by rental car. It may well be the only way.
It is indeed the only practicable way. The only alternative is a taxi or one of the very rare buses to Souillac, a train from there to Caussade (5 or 6 trains per day) but from there I can find nothing in the way of any transport to Saint-Antonin-Noble-Val.