Abstract: We analyze 7.3 yr of ANTARES high-energy neutrino and Fermi Large Area Telescope (LAT) gamma-ray data in search of cosmic neutrino + gamma-ray (nu + gamma) transient sources or source populations. Our analysis has the potential to detect either individual nu + gamma transient sources (durations delta t less than or similar to 1000 s), if they exhibit sufficient gamma-ray or neutrino multiplicity, or a statistical excess of nu + gamma transients of individually lower multiplicities. Individual high gamma-ray multiplicity events could be produced, for example, by a single ANTARES neutrino in coincidence with a LAT-detected gamma-ray burst. Treating ANTARES track and cascade event types separately, we establish detection thresholds by Monte Carlo scrambling of the neutrino data, and determine our analysis sensitivity by signal injection against these scrambled data sets. We find our analysis is sensitive to nu + gamma transient populations responsible for >5% of the observed gamma-coincident neutrinos in the track data at 90% confidence. Applying our analysis to the unscrambled data reveals no individual nu + gamma events of high significance; two ANTARES track + Fermi gamma-ray events are identified that exceed a once per decade false alarm rate threshold (p = 17%). No evidence for subthreshold nu + gamma source populations is found among the track (p = 39%) or cascade (p = 60%) events. Exploring a possible correlation of high-energy neutrino directions with Fermi gamma-ray sky brightness identified in previous work yields no added support for this correlation. While TXS.0506+056, a blazar and variable (nontransient) Fermi gamma-ray source, has recently been identified as the first source of high-energy neutrinos, the challenges in reconciling observations of the Fermi gamma-ray sky, the IceCube high-energy cosmic neutrinos, and ultrahigh-energy cosmic rays using only blazars suggest a significant contribution by other source populations. Searches for transient sources of high-energy neutrinos thus remain interesting, with the potential for either neutrino clustering or multimessenger coincidence searches to lead to discovery of the first nu + gamma transients.