travel from toulouse france to monpazier

At Toulouse-Blagnac Airport:

1 - take the shuttle to the city center and get off at the SNCF train station.
2 -Take the train to Bordeaux.
3 - In Bordeaux, take the train to Bergerac.
4 - In Bergerac, take a taxi to Monpazier or hitchhike.

Option 2:
Instead of taking the train from Toulouse to Bordeaux,

2 - take the train to Agen.
3 - In Agen, take a bus to Villeneuve-sur-Lot.
4 - In Villeneuve-sur-Lot, take a bus to Les Riviérettes.
5 -In Les Riviérettes, hitchhike.

Monpazier is a village of 450 inhabitants not served by public transportation, so be aware that once you arrive in Monpazier, without a car or a motorbike you won't have any means of transportation to get anywhere.

A car is essential in the Dordogne.

Honestly, I hope you can rent a car. Public transport within the Dordogne area is definitely not optimal. I would rent a car in Toulouse and return it in whatever city you are leaving from O(Toulouse? Bordeaux? ???). A car really is essential unless you are only staying in Monpazier, or have someone there who will drive you around to other towns.