Vault
Middle English: from Old French voute, based on Latin volvere ‘to roll’.
wiktionary
From Middle English vaute, vowte, from Old French volte (modern voûte), from Vulgar Latin *volta < *volvita or *volŭta, a regularization of Latin volūta (compare modern volute(“spire”)), the past participle of volvere(“roll, turn”). Cognate with Spanish vuelta(“turn”). Doublet of volute.
Borrowed from Middle French volter(“to turn or spin around; to frolic”), borrowed from Italian voltare, itself from a Vulgar Latin frequentative form of Latin volvere; later assimilated to Etymology 1, above.
etymonline
vault (n.1)
"arched roof or ceiling," c. 1300, vaute, from Old French voute "arch, vaulting, vaulted roof or chamber," from Vulgar Latin *volta, contraction of *volvita, noun use of fem. of *volvitus, alteration of Latin volutus "bowed, arched," past participle of volvere "to turn, turn around, roll," from PIE root *wel- (3) "to turn, revolve." The -l- appeared in English c. 1400, an etymological insertion in imitation of earlier forms (compare fault (n.), assault (n.)).
vault (v.1)
"jump or leap over," especially by aid of the hands or a pole, 1530s, transitive (implied in vaulting); 1560s, intransitive, from French volter "to gambol, leap," from Italian voltare "to turn," from Vulgar Latin *volvitare "to turn, leap," frequentative of Latin volvere "to turn, turn around, roll" (from PIE root *wel- (3) "to turn, revolve"). Related: Vaulted; vaulting.
vault (n.2)
"a leap," especially using the hands or a pole, 1570s, from vault (v.1).
vault (v.2)
"to form with a vault or arched roof," late 14c., from Old French vaulter, volter, from voute "arch, vaulted roof" (see vault (n.1)). Related: Vaulted; vaulting.