By a micro-experimental methodology, we study the ongoing molecular process inside coarse fibrin networks by means of microrheology. We made these networks gelate around a probe microbead, allowing us to observe a temporal evolution compatible with the well-known molecular formation of fibrin networks in four steps: monomer, protofibril, fiber and network. Thanks to the access that optical-trapping interferometry provides to the short-time scale on the bead's Brownian motion, we observe a Kelvin-Voigt mechanical behavior from low to high frequencies, range not available in conventional rheometry. We exploit that mechanical model for obtaining the characteristic lengths of the filamentous structures composing these fibrin networks, whose obtained values are compatible with a non-affine behavior characterized by bending modes. At very long gelation times, a omega (7/8) power-law is observed in the loss modulus, theoretically related with the longitudinal response of the molecular structures.