A contact tracing exercise has been put in place to try and find everyone who had recent connections with the two people.
The authorities launched the free testing service in places that are popular with tourists, both from France and those overseas, no details of the nationalities of the two people tested have been released.
More than 300 tests were undertaken in Issigeac last Thursday.
The positive Covid-19 results in Issigeac come just after the launch of a free testing operation at Bergerac Airport for passengers arriving in the Dordogne.
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