Fluorine (19F) abundances (or upper limits) are derived in six extragalactic AGB carbon stars from the HF(1-0) R9 line at 2.3358 mu in high resolution spectra. The stars belong to the Local Group galaxies LMC, SMC and Carina dwarf spheroidal, spanning more than a factor 50 in metallicity. This is the first study to probe the behaviour of F with metallicity in intrinsic extragalactic C-rich AGB stars. Fluorine could be measured only in four of the target stars, showing a wide range in F-enhancements. Our F abundance measurements together with those recently derived in Galactic AGB carbon stars show a correlation with the observed carbon and s-element enhancements. The observed correlations however, display a different dependence on the stellar metallicity with respect to theoretical predictions in low mass, low metallicity AGB models. We briefly discuss the possible reasons for this discrepancy. If our findings are confirmed in a larger number of metal-poor AGBs, the issue of F production in AGB stars will need to be revisited.