[en] Cool molecular hydrogen H₂ may be the ultimate possible constituent to the Milky-Way missing baryon. We describe a new way to search for such transparent matter in the Galactic disc and halo, through the diffractive and refractive effects on the light of background stars. By simulating the phase delay induced by a turbulent medium, we computed the corresponding illumination pattern on the earth for an extended source and a given passband. We show that in favorable cases, the light of a background star can be subjected to stochastic fluctuations of the order of a few percent at a characteristic time scale of a few minutes. We have searched for scintillation induced by molecular gas in visible dark nebulae as well as by hypothetical halo clumpuscules of cool molecular hydrogen (H₂-He) during two nights, using the NTT telescope and the IR SOFI detector. Amongst a few thousands of monitored stars, we found one light-curve that is compatible with a strong scintillation effect through a turbulent structure in the B68 nebula. Because no candidate were found toward the SMC (Small Magellan Cloud), we are able to establish upper limits on the contribution of gas clumpuscules to the Galactic halo mass. We show that the short time-scale monitoring of a few 10⁶ star*hour in the visible band with a >4 m telescope and a fast readout camera should allow one to interestingly quantify or constrain the contribution of turbulent molecular gas to the Galactic halo. (author)