Over the past decade, Magnetic Resonance Fingerprinting (MRF) has emerged as an efficient paradigm for the rapid and simultaneous quantification of multiple MRI parameters, including fat fraction (FF), water T1 ($T1_{H2O}$), water T2 ($T2_{H2O}$), and fat T1 ($T1_{fat}$). These parameters serve as promising imaging biomarkers in various anatomical targets such as the heart, liver, and skeletal muscles. However, measuring these parameters in the upper body poses challenges due to physiological motion, particularly respiratory motion. In this work, we propose a novel approach, motion-corrected (MoCo) MRF T1-FF, which estimates the motion field using an optimized preliminary motion scan and uses it to correct the MRF acquisition data before dictionary search for reconstructing motion-corrected FF and $T1_{H2O}$ parametric maps of the upper-body region. We validated this framework using an $\textit{in vivo}$ dataset comprising ten healthy volunteers and a 10-year-old boy with Duchenne muscular dystrophy. At the ROI level, in regions minimally affected by motion, no significant bias was observed between the uncorrected and MoCo reconstructions for FF (mean difference of -0.7%) and $T1_{H2O}$ (-4.9 ms) values. Moreover, MoCo MRF T1-FF significantly reduced the standard deviations of distributions assessed in these regions, indicating improved precision. Notably, in regions heavily affected by motion, such as respiratory muscles, liver, and kidneys, the MRF parametric maps exhibited a marked reduction in motion blurring and streaking artifacts after motion correction. Furthermore, the diaphragm was consistently discernible on parametric maps after motion correction. This approach lays the groundwork for the joint 3D quantification of FF and $T1_{H2O}$ in regions that are rarely studied, such as the respiratory muscles, particularly the intercostal muscles and diaphragm.