The EROS-2 project was designed to test the hypothesis that massive compact halo objects (the so-called ``machos) could be a major component of the dark matter halo of the Milky Way galaxy. To this end, EROS-2 monitored over 6.7 years $33times10^6$ stars in the Magellanic clouds for microlensing events caused by such objects. In this work, we use only a subsample of $7times10^6$ bright stars spread over $84 deg^2$ of the LMC and $9 deg^2$ of the SMC. The strategy of using only bright stars helps to discriminate against background events due to variable stars and allows a simple determination of the effects of source confusion (blending). The use of a large solid angle makes the survey relatively insensitive to effects that could make the optical depth strongly direction dependent. Using this sample of bright stars, only one candidate event was found, whereas $sim39$ events would have been expected if the Halo were entirely populated by objects of mass $Msim0.4M_{odot}$. Combined with the results of EROS-1, this implies that the optical depth toward the Large Magellanic Cloud (object{LMC}) due to such lenses is $tau<0.36times10^{-7}$ (95%CL), corresponding to a fraction of the halo mass of less than 8%. This optical depth is considerably less than that measured by the MACHO collaboration in the central region of the LMC. More generally, machos in the mass range $0.6times10^{-7}M_odot<M<15M_{odot}$ are ruled out as the primary occupants of the Milky Way Halo.
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