Context : Aims : We describe our newly developed approach to detailed abundance analysis from integrated-light high-dispersion spectra of star clusters . As a pilot project , we measure abundances of several Fe-peak , \alpha - and neutron capture elements from spectra of three globular clusters ( GCs ) in the Fornax dwarf spheroidal galaxy , obtained with UVES on the ESO Very Large Telescope . Methods : We divide the cluster colour-magnitude diagrams into about 100 bins and use the Kurucz ATLAS9 and SYNTHE codes to compute synthetic spectra for each bin . Stellar parameters are derived empirically from Hubble Space Telescope data for the brighter stars , while theoretical isochrones are used for extrapolation below the detection limit . The individual model spectra are co-added and the abundances are iteratively adjusted until the best match to the observed spectra is achieved . Results : We find [ Fe/H ] = -2.3 , -1.4 and -2.1 for Fornax 3 , 4 and 5 , with estimated \pm 0.1 dex uncertainties . Fornax 3 and 5 are thus similar in metallicity to the most metal-poor Milky Way GCs and fall near the extreme metal-poor end of the field star metallicity distribution in Fornax . The [ \alpha /Fe ] ratios , as traced by Ca and Ti , are enhanced with respect to the Solar composition at the level of \sim + 0.25 dex for Fornax 3 and 5 , and possibly slightly less ( \sim + 0.12 dex ) for Fornax 4 . For all three clusters the [ Mg/Fe ] ratio is significantly less elevated than [ Ca/Fe ] and [ Ti/Fe ] , possibly an effect of the abundance anomalies that are well-known in Galactic GCs . We thus confirm that Mg may be a poor proxy for the overall \alpha -element abundances for GCs . The abundance patterns of heavy elements ( Y , Ba and Eu ) indicate a dominant contribution to nucleosynthesis from the r -process in all three clusters , with a mean [ Ba/Eu ] \sim - 0.7 , suggesting rapid formation of the GCs . Conclusions : Combining our results with literature data for Fornax 1 and 2 , it is now clear that four of the five Fornax GCs fall in the range -2.5 < { [ Fe / H ] } < -2 , while Fornax 4 is unambiguously and substantially more metal-rich than the others . The indications that abundance anomalies are detectable in integrated light are encouraging , particularly for the prospects of detecting such anomalies in young , massive star clusters of which few are close enough for individual stars to be observed in detail .