The only free and comprehensive online etymological dictionary of the Spanish language
fruir (Verb) "to enjoy"
From Latin frui 'id.' From Proto-Italic *frūg-je/o- 'id.' From Proto-Indo-European *bhru̯g-i̯e/o- "to use."
Indo-European
Romance
Portuguese fruir, Catalan fruir, Italian fruire
fruta f. (Noun) "(a piece of) fruit"
13th cent. From fruto.
Indo-European
Romance
Asturian fruta, Portuguese fruta, Galician fruita, Catalan fruita, French fruit, Italian frutta
fruto m. (Noun) "fruit"
10th cent. From Latin fructus "enjoyment;" "fruit," derived from earlier frui "to enjoy" (see fruir).
Indo-European
Romance
Asturian frutu, Portuguese fruto, Galician froito, Catalan fruit, French fruit, Italian frutto, Aromanian frut, Romanian frupt, Sardinian frutu
Italic
Umbrian frif "fruits," Oscan fruktatiuf "usufruct"
Germanic
Gothic brukjan "to use," Old High German bruhhan 'id.,' Old Saxon brukan 'id.,' Old English brucan 'id.'
"The restriction to Gm. and It., and the pervading zero grade, may cast doubts on a PIE origin; yet there is no decisive argument against it." ~ M. de Vaan, Etymological Dictionary of Latin (2014)
fuego m. (Noun) "fire"
12th cent. From Late Latin focus 'id.,' from Latin focus "hearth." Of unknown origin.
Also the origin of the surnames Fuego, Fuejo and Fogón, originally given as a nickname to high-spirited individuals.
Indo-European
Romance
Asturian fueu, Portuguese fogo, Galician fogo, Catalan foc, French feu, Italian fuoco, Aromanian foc, Romanian foc, Sardinian fogu
fuente m. (Noun) "source;" "fount"
10th cent. From Latin fontem, accusative of fons "fountain." From Proto-Italic *fonti- "(water) spring." From Proto-Indo-European *dhonh2-ti̯- 'id.' From the root *dhenh2- "to flow."
Indo-European
Romance
Asturian fonte, Portuguese fonte, Galician fonte, Catalan font, French fonts, Italian fonte
Indo-Iranian
Sanskrit dhani "to flow"
Tocharian
A tsnāntär "to flow," B tsnamo "flowing"
fuera (Adverb) "outside"
10th cent. Old Spanish fueras; 12th cent. fuera. From Latin foras 'id.' From Proto-Italic *forā- "to the door," accusative case of Proto-Indo-European *dhu̯ō̆r-h2- "doors" in either the dual or as an ancient plurale tantum (see note under -a).
Indo-European
Romance
Portuguese fora, Galician fóra, Catalan fora, Italian fuori, Aromanian fãrã, Romanian fără
Celtic
Old Irish dorus, Old Welsh dor, Middel Breton dor, Cornish dor
Germanic
Gothic daur, Old Norse dyrr, Old High German turi, Old Saxon dor, Old English dor (English door)
Balto-Slavic
Old Church Slavonic dvьrь, Lithuanian dùrys, Albanian derë
Hellenic
Ancient Greek θυρᾱ (thura), Mycenaean *tu-ra-
Armenian
Armenian dowr-k'
Indo-Iranian
Sanskrit dvā́r-, Young Avestan duuar-
Tocharian
B twere
fuero m. (Noun) "historic law;" "jurisdiction"
10th cent. From Latin forum "forum." From Proto-Italic *fworo- "vestibule." From Proto-Indo-European *dhu̯or-o- "door." Probably developing in a sense of a room with doors becoming a public venue.
Indo-European
Romance
Portuguese foro, Catalan forum, French for, Italian foro, Romanian for
Italic
Umbrian furu
Celtic
Gaulish Augusto-durum (Roman name for the city of Bayeux) "Augustine's forum"
Balto-Slavic
Old Church Slavonic dvorъ "court," Lithuanian dvãras 'id.'
Indo-Iranian
Sanskrit dvāram "passage"
fuerte m. (Adjective, Noun, Adverb) "strong;" "fort;" "loudly"
As an adjective first attested in the 10th cent; as a noun, 16th cent. From Latin fortis "strong." From Proto-Italic *forkt-i/o- 'id.' From either *bhorg-to-, *dhorg-to-, or *gwhork-to- 'id.' in Proto-Indo-European, with three possible ancestral consonants.
Indo-European
Romance
Asturian fuerte, Portuguese forte, Galician fuerte, Catalan fort, French fort, Italian forte, Romanian foarte
Italic
Oscan fortis
Celtic
Gaulish -briga "hill," Old Irish brí 'id.,' Middle Welsh bre 'id.,' Middle Breton bre 'id.,' Cornish bre
Germanic
Gothic bairgahei "mountainous," Old Norse bjarg "mountain," Old High German berg 'id.,' Old Saxon berg 'id.,' Old English beorg 'id.' (English barrow)
Balto-Slavic
Lithuanian dir̃žti "to harden," Latvian derža (?) "whip," of uncertain etymology
Armenian
Armenian barjr "high"
Indo-Iranian
Sanskrit barh- "to make strong," Young Avestan barəzah- "height"
Tocharian
A pärkär "long"
fuerza f. (Noun) "force"
Early 12th cent. From Late Latin fortia 'id.,' the neuter plural of fortis "strong" (see fuerte for further etymology).
Indo-European
Romance
Asturian fuerte, Portuguese forte, Galician fuerte, Catalan fort, French fort, Italian forte, Romanian foarte
fui, fue, fui-, fuer-, fues- Preterite, imperfect, and future conjugation stems in verbs ser and ir.
From their respective forms in Latin fui, fue, fui-, fuer-, fues- with the meaning of "become."

From Proto-Italic stem *fu- "to become." From Proto-Indo-European *bhh2u̯- 'id.'

Note that present and future indicative derive from Latin sedere "to sit." The verb collapsed sedere and essere "to be" with fui into a single new verb meaning "to be."
The forms appearing in ir were drawn from the verb ser.