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Le Vieux Port has WiFi access, available from many of the bars and restaurants, and in some places in the street although there are not many places to sit. The ESSID to use is "Marseille sans fil" and the network is not encrypted. When you first connect, your browser will take you to a web page about the service in French: simply click on "Cliquez ici" "Click here" on that page to use the network freely.
Note WiFi is pronounced wee-fee or wiffy in French - even by English speakers. Asking for Why-Fye will usually be greeted by a blank look.