Fano resonance observed in various classical and quantum systems features an asymmetric spectral line shape. For designing nanoresonators for monochromatic applications, it is beneficial to describe Fano resonance in non-spectral parametric domains of critical structural parameters. We develop an analytical model of the parametric Fano profile based on a coupled harmonic oscillator model and theoretically demonstrate its application in describing the optical response of a series of waveguided plasmonic crystals of varying periodicity. The developed parametric Fano model may find applications in the design of monochromatic and spectrometer-free nanodevices.