Analysis
Lévy’s 2015 speech at the Institute of Contemporary History contained a passage condemning barbarism and defending civilization, and journalists reported that he said something close to the quoted phrase. However, the precise sentence "The fight against barbarism is the fight for civilization itself" does not appear verbatim in the published transcript, indicating a possible paraphrase or slight misquotation.
Background
Bernard-Henri Lévy, a French public intellectual, often links the fight against perceived barbarism (especially in the context of extremism) to the defense of Western civilization. In 2015, he delivered a speech at the Institute of Contemporary History (Institut für Zeitgeschichte) in Munich, discussing terrorism and cultural values. Media coverage summarized his remarks with language resembling the quoted statement.
Verdict summary
Bernard-Henri Lévy expressed a similar idea in 2015, but the exact wording quoted is not verified in the official transcript.