Accurate control of both the doping distribution inside the fiber core and the low refractive index contrast between the fiber core and cladding materials is essential for the development of high-power fiber lasers based on the use of single-mode large-mode-area (LMA) optical fibers. Herein, sol-gel monolithic F/Yb3+-codoped silica glasses were prepared from porous large silica xerogels doped with ytterbium salt solution, which had been subjected to fluorination with hexafluoroethane gas, before subsequent sintering. The fluorine content inside the doped glass has been varied by adjusting the fluorination duration. The space homogeneity of fluorine and ytterbium concentrations in the cylindrical preforms has been checked by chemical analysis and Raman spectroscopy. Moreover, the glass with the lowest fluorine content has been successfully integrated as a core material in a microstructured optical fiber made using the stack-and-draw method. This fiber was tested in an all-fiber cavity laser architecture to evaluate potential lasing performances of the F/Yb3+-codoped silica glass. It presents a maximum efficiency of 70.4%, achieved at 1031 nm from a 1.16 m length fiber. These results confirm the potentialities of the obtained F/Yb3+-codoped glasses for the fabrication of LMA optical fiber lasers.