Context : The formation process of binary stars and multiple systems is poorly understood . The multiplicity rate of Class II pre-main-sequence stars and Class I protostars is well documented and known to be high ( \sim 30 % to 50 % between \sim 100 and 4000 AU ) . However , optical / near-infrared observations of Class I/Class II YSOs barely constrain the pristine properties of multiple systems , since dynamical evolution can quickly alter these properties during the protostellar phase . Aims : Here , we seek to determine the typical outcome of protostellar collapse and to constrain models of binary formation by core fragmentation during collapse , using high-resolution millimeter continuum imaging of very young ( Class 0 ) protostars observed at the beginning of the main accretion phase . Methods : We carried out a pilot high-resolution study of 5 Class 0 objects , including 3 Taurus sources and 2 Perseus sources , using the most extended ( A ) configuration of the IRAM Plateau de Bure Interferometer ( PdBI ) at 1.3 mm . Our PdBI observations have a typical HPBW resolution \sim 0.3 ″– 0.5 ″ and rms continuum sensitivity \sim 0.1 – 1 mJy/beam , which allow us to probe the multiplicity of Class 0 protostars down to separations a \sim 50 AU and circumstellar mass ratios q \sim 0.07 . Results : We detected all 5 primary Class 0 sources in the 1.3 mm dust continuum . A single component associated with the primary Class 0 object was detected in the case of the three Taurus sources , while robust evidence of secondary components was found toward the two Perseus sources : L1448-C and NGC1333-IR2A . We show that the secondary 1.3 mm continuum component detected \sim 600 AU south-east of L1448-C , at a position angle close to that of the CO ( 2–1 ) jet axis traced by our data , is an outflow feature directly associated with the powerful jet driven by L1448-C . The secondary 1.3 mm continuum component detected \sim 1900 AU south-east of NGC1333-IR2A may either be a genuine protostellar companion or trace the edge of an outflow cavity . Therefore , our PdBI observations revealed only wide ( > 1500 AU ) protobinary systems and/or outflow-generated features . Conclusions : When combined with previous millimeter interferometric observations of Class 0 protostars , our pilot PdBI study tentatively suggests that the binary fraction in the \sim 75 – 1000 AU range increases from the Class 0 to the Class I stage . It also seems to argue against purely hydrodynamic models of binary star formation . We briefly discuss possible alternative scenarios to reconcile the low multiplicity rate of Class 0 protostars on small scales with the higher binary fraction observed at later ( e.g . Class I ) evolutionary stages .