The interaction of a 2D metal-organic network (MON) stacked on graphene has been studied with the help of first-principles density functional theory (DFT) and DFT+U calculations. By varying the length of a polyphenyl-dicarbonitrile linker, we have evaluated the influence of the metal-metal distance on the electronic and magnetic properties of the MON complexes. Although MON composed of small molecules shows a moderately stable ferromagnetic phase, this magnetic order drops with the size of the complex. After the adsorption of MON on graphene, this last becomes n-doped due to an important charge transfer that improves with the molecular unit size. The MON-graphene interaction contributes to drastically reduce the overall stability of any magnetic order, but the local charge transfer remains strongly spin-polarized-dependent. Hence, the adsorption of magnetic MON on graphene leads to the modification of the electronic and magnetic properties of graphene, mostly in a closed proximity region to the active metal atoms of the MON. Spin-polarized scanning tunneling microscopy simulations reveal a magnetic signature in graphene that originates from its interaction with the MONs and that could be experimentally observed.