Context. Fornax is one of the most massive dwarf spheroidal galaxies in the Local Group. The Fornax field star population is dominated by intermediate age stars but star formation was going on over almost its entire history. It has been proposed that Fornax experienced a minor merger event. Aims: Despite recent progress, only the high metallicity end of Fornax field stars ([Fe/H] > -1.2 dex) has been sampled in larger number via high resolution spectroscopy. We want to better understand the full chemical evolution of this galaxy by better sampling the whole metallicity range, including more metal poor stars. Methods: We use the VLT-FLAMES multi-fibre spectrograph in high-resolution mode to determine the abundances of several α, iron-peak and neutron-capture elements in a sample of 47 individual red giant branch stars in the Fornax dwarf spheroidal galaxy. We combine these abundances with accurate age estimates derived from the age probability distribution from the colour-magnitude diagram of Fornax. Results: Similar to other dwarf spheroidal galaxies, the old, metal-poor stars of Fornax are typically α-rich while the young metal-rich stars are α-poor. In the classical scenario of the time delay between Type II (SNe II) and Type Ia Supernovae (SNe Ia), we confirm that SNe Ia started to contribute to the chemical enrichment at [Fe/H] between -2.0 and -1.8 dex. We find that the onset of SNe Ia took place between 12-10 Gyr ago. The high values of [Ba/Fe], [La/Fe] reflect the influence of SNe Ia and AGB stars in the abundance pattern of the younger stellar population of Fornax. Conclusions: Our findings of low [α/Fe] and enhanced [Eu/Mg] are compatible with an initial mass function that lacks the most massive stars and with star formation that kept going on throughout the whole history of Fornax. We find that massive stars kept enriching the interstellar medium in α-elements, although they were not the main contributor to the iron enrichment. Based on FLAMES observations collected at the European Southern Observatory, proposal number 080.B-0784.Table 7 is only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/572/A88Appendices are available in electronic form at http://www.aanda.org