Controlling droplet shape via surface tension has numerous technological applications, such as droplet lenses and lab-on-a-chip. This motivates a partial differential equationconstrained shape optimization approach for controlling the shape of droplets on flat substrates by controlling the surface tension of the substrate. We use shape differential calculus to derive an L-2 gradient flow approach to compute equilibrium shapes for sessile droplets on substrates. We then develop a gradient-based optimization method to find the substrate surface tension coefficient yielding an equilibrium droplet shape with a desired footprint (i.e., the liquid-solid interface has a desired shape). Moreover, we prove a sensitivity result with respect to the substrate surface tensions for the free boundary problem associated with the footprint. Numerical results are also presented to showcase the method.