Integrating fluorescence sensing with silicon photonic platforms holds great potential for on-chip molecular detection, but so far it is hindered by weak waveguide-collected fluorescence and unreliable spectral information. We propose and demonstrate an on-chip fluorescence sensing paradigm by hybrid integrating fluorescent materials with silicon-on-insulator (SOI) microring resonators. Unlike integrating with straight waveguides, the microring resonator modulates broadband fluorescence into discrete high-quality (Q = 3476.7) resonant peaks, concurrently enhancing signal-to-noise ratio (SNR) and spectral fidelity. This modulation enables a synergistic dual-mode amplification mechanism within a single microring resonator: where the resonance wavelength shift from refractive-index variations and the intensity quenching from chemical responses cooperate to mutually boost the sensing output. It is first experimentally demonstrated in an SOI based on-chip sensor with a 1 ppb detection limit, accompanied by the first theoretical model clarifying this synergistic effect. Beyond sensitivity enhancement, the dual-mode synergy provides multi-dimensional discriminative parameters (wavelength shift, peak intensity variation, and overall fluorescence intensity variation), fundamentally improving sensing accuracy for gas species with similar fluorescence quenching behaviors. This work offers a promising route to a high-performance on-chip fluorescence sensor via a standard SOI-compatible technique.