Take bus lines 82 or 83 and get off at the "Pharo" stop. (7mn)
From St Charles Train Station (and Bus Station):
Under the station, go down to the metro and take line M1 "La Rose - La Fourragère" (blue line) in the direction of La Fourragère. Get off at "Vieux-Port / Hôtel de Ville" station. Follow the "Vieux-Port" exit (take the escalators up, go straight, then after the second escalators, turn right).
Once at the Vieux-Port, you can take an RTM bus.
The "Métro Vieux-Port" bus stop is 30 meters in front of the metro exit.
Then, take the bus (see above: "From Vieux-Port").
By foot: The palace is a short walk from the Vieux-Port