Baur originally intended to become a sailor but instead opted to pursue a career as an actor. Having been turned down by the Paris Conservatory, he took private lessons in drama and was soon appearing in stage productions in Marseilles. This led to a series of engagements in Paris, where he quickly became a sought after stage actor.
He appeared in a number of silent films, including Michel Carré's Les Suicides de Louf, Shylock (1913), Abel Gance's Strass et Compagnie (1915), Henry Roussell's L'Âme du bonze (1918), and Léon Abrams La Voyante (1923) which also featured the final film appearance by Sarah Bernhardt. Perhaps disillusioned with the medium, he returned to stage acting and scored some notable successes, most notably in Marcel Pagnol's Jazz.
Towards the end of the decade, he was persuaded by Julien Duvivier to return to cinema, which had just entered the sound era. The film in question was David Golder (1930), which was to be the first of Baur's great film successes. Around this time, he lost both his 20-year old son and his wife, a double tragedy which no doubt contributed towards his intensely morose and commanding performances in Le Juif polonais (1931) and Poil de Carotte (1932).
Over the next decade, Harry Baur would become one of France's leading film actors. His most memorable roles included Inspecteur Maigret in Duvivier's La Tête d'un homme (1933), Jean Valjean in Raymond Bernard's Les Misérables (1933) and Raspoutine in Marcel L'Herbier's La Tragédie impériale (1938). Other successes included Un grand amour de Beethoven (1936) and Maurice Tourneur's Volpone (1941).
At the time of the Nazi occupation, Baur was denounced as a Jew and freemason by collaborators, and was forced into working for the German-run film company Continental. Having made some public pro-French statements, he set out to Germany to make what would be his last film, Sinfonie eines Lebens (1942). Then, in May 1942, he was arrested by the German police and tortured. Four months later, he was released, visibly weakened by his experiences at the hands of the Gestapo. Not long after, he died under mysterious circumstances, on 8th April 1943. His suspicious death galvanised anti-German sentiment in France, whilst his funeral provoked a great public outpouring of grief.