Estival and festival look so much alike that you might think they're very closely related, but that isn't the case. Estival traces back to aestas, which is the Latin word for "summer" (and which also gave us estivate, a verb for spending the summer in a torpid state—a sort of hot-weather equivalent of hibernating). Festival also comes from Latin, but it has a different and unrelated root. It derives from festivus, a term that means "festive" or "merry." Festivus is also the ancestor of festive and festivity as well as the much rarer festivous (which also means "festive") and infestive ("not merry, mirthless").
Word History
Etymology
Middle English, from Anglo-French or Latin; Anglo-French, from Latin aestivalis, from aestivus of summer, from aestas summer — more at edify