French media reported that the state-owned museum in Elne in the south of France could have spent as much as €160,000 (£140,000) on the forgeries over a 20-year period.
Staff at the museum were unaware of the fakes until art historian Eric Forcada flagged his suspicions several months ago.
He noticed some of the buildings shown in the drawings and watercolours were erected following the artist’s death in 1922.
A group of experts reportedly inspected the works of art and confirmed 82 of the 140 pieces were not produced by Terrus.
The Mayor of Elne, Yves Barniol, called the situation “a catastrophe” on Friday as it was announced when the museum opened following a renovation.
He apologised to those who had visited the museum and thought they had seen genuine works of art by Terrus.
France Bleu reported him as saying: “I put myself in the place of all the people who came to visit the museum, who saw fake works, who took a ticket of entry, whatever the price.
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“It is unacceptable and I hope we find those responsible.”
Police in France have now launched an investigation into allegations of fraud and forgery and have warned other regional artists and museums may have fallen victim to counterfeiting too.