This paper describes new results on the identification of the complex gravitational lens responsible for the double quasar Q2345+007. A gravitational shear field was detected recently about 45" away from the QSO, centered on an excess of faint blue galaxies. The redshift distribution is still unknown, so the mass and the photometric properties of the deflector are still a matter of debate. We present deep photometric data obtained in the near-IR (J and K'), which are used together with preexisting optical BRI photometry to build spectral energy distributions for all the objects of the field, and to derive a photometric redshift estimate by comparison with synthetic spectrophotometric data. We propose a statistical method to analyse the redshift distribution, based on the cumulative histogram of the redshift ranges allowed for the different objects. An excess of galaxies at a redshift of z=~0.75 is clearly detected in the field of Q2345+007, with a 2D distribution showing a maximum located at the center of the weak shear field. Besides, the redshift inferred for this cluster is also compatible with that found for an absorption system in the spectrum of the B component of the quasar. We interpret this overdensity of objects as a distant cluster of galaxies responsible for the gravitational shear field. Two other redshift concentrations are studied: z=0.28 which corresponds to the spectroscopic redshift of three galaxies but for which no strong excess of objects is identified, and z=~1.2, where an excess of galaxies is also detected, but with a rather smooth 2D distribution over our field of view. We also discuss the existence of other possible excesses of galaxies at redshift planes compatible with the absorption systems detected in the spectra of the QSOs. Most cluster-member candidates at z=~0.75 are undergoing a star-formation process or are burst systems where the star formation stopped between 1 and 3Gyr ago.