Development of graphene spintronic devices relies on transforming it into a material with a spin order. Attempts to make graphene magnetic by introducing zigzag edge states have failed due to energetically unstable structure of torn zigzag edges. Here, we report on the formation of nanoridges, i.e., stable crystallographically oriented fluorine monoatomic chains, and provide experimental evidence for strongly coupled magnetic states at the graphene-fluorographene interfaces. From the first principle calculations, the spins at the localized edge states are ferromagnetically ordered within each of the zigzag interface whereas the spin interaction across a nanoridge is antiferromagnetic. Magnetic susceptibility data agree with this physical picture and exhibit behaviour typical of quantum spin-ladder system with ferromagnetic legs and antiferromagnetic rungs. The exchange coupling constant along the rungs is measured to be 450 K. The coupling is strong enough to consider graphene with fluorine nanoridges as a candidate for a room temperature spintronics material.