As Nicolas75 says, it not a really dangerous area as such, although it is hardly an attractive one either. Certainly, there are no issues during the day. Nighttime might be sketchier but you need to apply usual common-sense large city prudent behaviour: be aware of your surroundings; avoid walking down unlit side-streets; appear clear and purposeful about where you are going, don't look like an obvious lost tourist, etc...

There is no area in the immediate vicinity of where you are which would be a no-go area as such. Again, use common sense to determine whether you feel comfortable or not walking a particular street at a particular time. The more difficult areas of Marseille are further North, in some "cités" (="projects" in US english; "estates" in UK English) of the "quartiers nord".

In my days, the Belle-de-Mai district, just North of Gare St Charles, was a kind of transition area between Central Marseille and the "quartiers nord" beyond which no middle-class mother would have liked her sons, still less her daughters, to walk unaccompanied. These days, I understand that Belle-de-Mai is in the process of gentrification, so the 'border' might have moved further North.

None of these areas would be of any interest to a tourist anyway so you would have no reason to venture North.