The Celtic festival considered a time when the fairy world is most accessible is Samhain.
Samhain was one of the four major festivals of the Gaelic calendar, marking the end of harvest and the beginning of winter. In Irish mythology, it was a liminal threshold when the boundary between the human world and the Otherworld became easier to cross. The aos sí, or fairy people, could emerge, while the dead were also believed to revisit their homes.
Medieval Irish tradition gives Samhain an especially strong supernatural setting. The Boyhood Deeds of Fionn says that fairy mounds, understood as portals to the Otherworld, were always open at Samhain. Tales describe beings emerging from sites such as the Cave of Cruachan and the mound of Slievenamon.
Bealtaine is another threshold festival and is sometimes associated with supernatural encounters, so the two can be confused. Samhain is the stronger conventional answer because its folklore emphasizes the dead, fairy hosts, open portals, and the dangers of the dark half of the year. Modern Halloween customs developed partly from this seasonal tradition.