Single-molecule fluorescence spectroscopy of freely diffusing molecules in solution is a powerful tool used to investigate the properties of individual molecules. Single-Photon Avalanche Diodes (SPADs) are the detectors of choice for these applications. Recently a new type of SPAD detector was introduced, dubbed red-enhanced SPAD (RE-SPAD), with good sensitivity throughout the visible spectrum and with excellent timing performance. We report a characterization of this new detector for single-molecule fluorescence resonant energy transfer (smFRET) studies on freely diffusing molecules in a confocal geometry and alternating laser excitation (ALEX) scheme. We use a series of doubly-labeled DNA molecules with donor-to-acceptor distances covering the whole range of useful FRET values. Both intensity-based (μs-ALEX) and lifetime-based (ns-ALEX) measurements are presented and compared to identical measurements performed with standard thick SPADs. Our results demonstrate the great potential of this new detector for smFRET measurements and beyond.