"Algiers" is a romantic mystery starring Charles Boyer and Hedy Lamarr. It's a 1938 Hollywood remake of the 1937 French film "Pepe le Moko" with Jean Gabin. Pepe (Boyer) is a notorious thief who has escaped from France and hides in the Casbah of Algiers. The French officials are after him, but he is protected by the local police. Boyer and Lamarr are attractive, and in one scene Boyer sings "C'est la vie" to his neighbours. See: http://en.wikipedia.org/wiki/Algiers_%28film%29
You can stream Algiers (1938) free and legally on OldReel, via the Internet Archive.
Yes — it is in the public domain and can be watched and shared freely.