As part of our efforts to unveil extragalactic large-scale structures behind the southern Milky Way, we here present redshifts for 764 galaxies in the Hydra/Antlia, Crux and Great Attractor region (266{deg}<=l<=338{deg}, |b|<=10{deg}), obtained with the Meudon-ESO Fibre Object Spectrograph (MEFOS) at the 3.6-m telescope of ESO. The observations are part of a redshift survey of partially obscured galaxies recorded in the course of a deep optical galaxy search behind the southern Milky Way (Kraan-Korteweg 2000, Cat. <J/A+AS/141/123>; Woudt & Kraan-Korteweg 2001, Cat. <J/A+A/380/441>). A total of 947 galaxies have been observed, a small percentage of the spectra (N=109, 11.5%) were contaminated by foreground stars, and 74 galaxies (7.8%) were too faint to allow a reliable redshift determination. With MEFOS we obtained spectra down to the faintest galaxies of our optical galaxy survey, and hence probe large-scale structures out to larger distances (v<=30000km/s) than our other redshift follow-ups using the 1.9-m telescope at the South African Astronomical Observatory (Kraan-Korteweg et al., 1995, Cat. <J/A+A/297/617>; Fairall et al., 1998, Cat. <J/A+AS/127/463>; Woudt et al., 1999, Cat. <J/A+A/352/39>) and the 64-m Parkes radio telescope (Kraan-Korteweg et al., 2002, Cat. <J/A+A/391/887>). The most distinct large-scale structures revealed in the southern Zone of Avoidance are discussed in context to known structures adjacent to the Milky Way.