Remote sensing employs solar-induced chlorophyll fluorescence (SIF) as a proxy for photosynthesis from field to airborne and satellite sensors. The investigation of SIF offers a unique way of studying vegetation functioning from the local to the global scale. However, the passive, optical retrieval of the SIF signal is still challenging. Common retrieval approaches extract the SIF infilling directly from atmospheric oxygen bands in down-welling and up-welling radiance. They often involve a complex signal correction to compensate for atmospheric reabsorption and require long computing time. In contrast, the exploitation of solar Fraunhofer lines is devoid of atmospheric disturbances. We propose a new retrieval method for red and far-red SIF directly from up-welling radiance spectra in the spectral range between 650 nm and 810 nm by applying Partial Least Squares (PLS) regression machine learning. Solar Fraunhofer lines are exploited for SIF retrieval with the PLS approach by excluding telluric absorption features. The PLS models are trained and tested on synthetic reflectance and SIF data modeled with SCOPE. We identified a logarithmic relationship of the retrieval error with respect to signal-to-noise ratio of the instrument. The approach has been tested with real-world data measured by the Fluorescence Box (FloX), and evaluated against two well-established retrieval methods: the spectral fitting method (SFM) and the singular value decomposition (SVD). PLS models exploiting solar Fraunhofer lines retrieved meaningful SIF values with high precision and demonstrated robustness against atmospheric reabsorption, including from a 100m tall tower. In addition, PLS retrieval requires no complex correction for atmospheric reabsorption and computes 37 times faster than SFM. Hence, PLS retrieval allows fast and robust exploitation of SIF from solar Fraunhofer lines with high precision under conditions in which other retrieval approaches require complex atmospheric correction.