We studied electric field modification of magnetic properties in a Pt/Co/AlO$_x$ trilayer via magneto-optical Kerr microscopy. We observed the spontaneous formation of labyrinthine magnetic domain structure due to thermally activated domain nucleation and propagation under zero applied magnetic field. A variation of the period of the labyrinthine structure under electric field is observed as well as saturation magnetization and magnetic anisotropy variations. Using an analytical formula of the stripe equilibrium width we estimate the variation of the interfacial Dzyaloshinskii-Moriya interaction under electric field as function of the exchange stiffness constant.