As part of the Panchromatic Exoplanet Treasury program, we have conducted a spectroscopic study of WASP-79b, an inflated hot Jupiter orbiting an F-type star in Eridanus with a period of 3.66 days. Building on the original WASP and TRAPPIST photometry of Smalley et al., we examine Hubble Space Telescope (HST)/Wide Field Camera 3 (WFC3) (1.125–1.650 μm), Magellan/Low Dispersion Survey Spectrograph (LDSS)-3C (0.6–1 μm) data, and Spitzer data (3.6 and 4.5 μm). Using data from all three instruments, we constrain the water abundance to be −2.20 ≤ log(H2O) ≤ −1.55. We present these results along with the results of an atmospheric retrieval analysis, which favor inclusion of FeH and H− in the atmospheric model. We also provide an updated ephemeris based on the Smalley, HST/WFC3, LDSS-3C, Spitzer, and Transiting Exoplanet Survey Satellite (TESS) transit times. With the detectable water feature and its occupation of the clear/cloudy transition region of the temperature/gravity phase space, WASP-79b is a target of interest for the approved James Webb Space Telescope (JWST) Director’s Discretionary Early Release Science (ERS) program, with ERS observations planned to be the first to execute in Cycle 1. Transiting exoplanets have been approved for 78.1 hr of data collection, and with the delay in the JWST launch, WASP-79b is now a target for the Panchromatic Transmission program. This program will observe WASP-79b for 42 hr in four different instrument modes, providing substantially more data by which to investigate this hot Jupiter.