For a given dimension d $\ge$ 2 and a finite measure $ν$ on (0, +$\infty$), we consider $ξ$ a Poisson point process on R d x (0, +$\infty$) with intensity measure dc $\otimes$ $ν$ where dc denotes the Lebesgue measure on R d. We consider the Boolean model $Σ$ = $\cup$ (c,r)$\in$$ξ$ B(c, r) where B(c, r) denotes the open ball centered at c with radius r. For every x, y $\in$ R d we define T (x, y) as the minimum time needed to travel from x to y by a traveler that walks at speed 1 outside $Σ$ and at infinite speed inside $Σ$. By a standard application of Kingman sub-additive theorem, one easily shows that T (0, x) behaves like $μ$ x when x goes to infinity, where $μ$ is a constant named the time constant in classical first passage percolation. In this paper we investigate the regularity of $μ$ as a function of the measure $ν$ associated with the underlying Boolean model.