We present a minimal model of spray combustion to investigate a flame front propagating through a fuel-lean mixture of fuel vapor, droplets and air. The model relies on a main control parameter, Da, named the Damkoehler number, which allows us to take into account a large variety of fuel sprays. Numerical results reveal, as a function of Da, a wide range of spray-flame structures, including the classical gaseous premixed flame, a specific regime controlled by vaporisation, and a pulsating mode of propagation. The latter appears when the vaporisation is smaller than (or equal to) the reaction time, and it occurs even with a unit Lewis number.