French foreign ministry spokesman Philippe Lalliot declined to give details of the circumstances surrounding the deaths of the two people but confirmed that one was French.
The Europeans were chased after local residents found the remains of a child with his organs removed, the interior ministry official said.
The crowd caught them, hanged them and burnt their bodies on the Nosy Be beach, he said.
“We are counting on the Malagasy authorities to bring to light the exact circumstances of this and have asked them to take measures to increase security for our nationals on the ground, given that Nosy Be is a popular tourist destination,” Mr Lalliot told a news briefing.
Nosy Be is an island off the northwestern tip of mainland Madagascar famed for its turquoise waters and white-sand beaches and one of the Indian Ocean island’s leading tourism hubs.
Mr Lalliot said that French nationals had been warned to remain vigilant and the French school had been temporarily closed.
Malagasy officials were not immediately available for comment.
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