Context. The ratio of the first overtone (1O) / fundamental (F) periods of mixed-mode Cepheids that pulsate simultaneously in these two modes (F/1O) is metallicity-dependent. It can therefore be used to characterize the systems that host such variable stars-Aims. We want to take advantage of the F/1O double-mode Cepheids listed in the Gaia DR2 catalogue to derive the metallicity gradient in the Milky Way disk. Methods. The metallicity is derived from the ratio of the first overtone and fundamental periods provided by Gaia DR2 while the Gaia DR2 parallaxes are used to determine the Galactocentric distances of the stars. Results. From a visual inspection of the light curves, it turns out that a large fraction (77%) of the Galactic F/1O double-mode Cepheids in Gaia DR2 are spurious detections. Gaia DR2 provides 3 new bona fide F/1O Cepheids. Combining them with the currently known F/1O Cepheids and using the Gaia DR2 parallaxes for the entire sample, we can derive the metallicity gradient in the Milky Way disk. We find a slope of-0.045±0.007 dex/kpc using a bootstrap method, and of -0.040±0.002 dex/kpc using a total least squares method. These results are in good agreement with previous determinations of the [Fe/H] gradient in the disk based on canonical Cepheids. Conclusions. The period ratio of F/1O Cepheids allows for a reliable determination of the metallicity gradient in the Milky Way, and in turn, in other systems that would be difficult to reach via classical spectroscopic methods.In Petersen diagrams, it has been known for a long time that the period ratios fall around P 21 = P 2 /P 1 = 0.80 for the Cepheids pulsating simultaneously in the first and second overtone modes (1O/2O), and around P 10 = P 1 /P 0 = 0.72 for the Cepheids pulsating simultaneously in the fundamental and first overtone modes (F/1O). Moreover, the period-ratios are different for the F/1O double-mode Cepheids located in the Milky Way, the LMC and the SMC, and these stars occupy different regions