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It depends how much you want to soak it in, how many pics, beers and the level of wandering off you want to do. I've done it in a week, but would love to do it in twice as long (stopping one or two days in La Brigue, loved that place).
The logistics that come with the route can be constraining in a way that you still have to do a given amount of km every day, unless you fancy camping atop a windy pass.
How long do you reckon it'd take at a more relaxed pace? I might try to squeeze in a solo-non-race version if I have time.