The only free and comprehensive online etymological dictionary of the Spanish language
fábrica f. (Noun) "factory"

15th cent. Borrowed from Latin fabrica "workshop." The native descendent of fabrica is fragua.

Romance: Western Vulgar Latin: Catalan fàbrica, French fabrique, Italian fabbrica; Eastern Vulgar Latin: Romanian fabrică; Sardinian: fravica
fabro m. (Noun) (obsolete) "artisan"

From Latin fabrum, accusative of faber 'id.' Dissimilated from Proto-Italic *fafro- 'id.' From Proto-Indo-European *dhHbh-ro- "craftsman."

Still in use as the surnames Fabro, Fabros.

Romance: Western Vulgar Latin: Portuguese fabro, Italian fabbro; Eastern Vulgar Latin: Aromanian favru, Romanian faur; Sardinian: frau, frab, frabbu

Indo-European: Armenian: darbin "smith"

If fabro and its cousins are etymologically related to a smattering of words found in Baltic (Lithuanian dabà "nature"), Slavic (Old Church Slavonic podoba "ornamentation"), and Germanic (Gothic gadof "fitting," "right"), then Beekes (1996) believes all of these words must be borrowed from a non-Indo-European language with a root *dhabh-.
fábula f. (Noun) "fable," "rumor"

A learned borrowing from Latin fabula 'id.,' from fari "to talk" and instrumental suffix -bula. The native word in Spanish is habla.

Romance: Western Vulgar Latin: Portuguese fábula, French fable, Italian favola
fácil (Adjective) "easy"

From Latin facilis 'id.' Formed from facere "to make" and -ilis, a suffix indicating a relational state (see hacer and -il respectively).

Romance: Western Vulgar Latin: Portuguese fácil, Galician fácil, Catalan fácil, French facile, Italian facile
fallar (Verb) "to fail"

From Latin fallare "to deceive," "to mistake." From Proto-Italic *faln-e/o- 'id.' From Proto-Indo-European *sgwhel-n- "to stumble."

According to Tibón (1988), also the origin of the surname de Falla, when the so-named is not from Valencia, but the origin account is passed over without comment.

Romance: Western Vulgar Latin: Portuguese falhar, French faillir, Italian fallare

Indo-European: Hellenic: Ancient Greek σφάλλομαι (shállomai) "to fall," "to be ruined;" Armenian: sxalem "to fail;" Indo-Iranian: Sanskrit skhalate "to stumble," Middle Persian škarwīdan 'id.'
falta f. (Noun) "absence;" "fault"

13th cent. From Vulgar Latin *fallita 'id.,' from fallere "to deceive," "to mistake" (see fallar).
faltar (Verb) "to fault"

14th cent. From Latin faltare 'id.,' from fallere "to deceive" (see fallar) and -tare, frequentive suffix (see note under faltar.

The frequentive suffixes in Latin indicated repeated actions. Suffixes like these are akin to the English suffix -le, in words like joust ~ jostle and mud ~ muddle. The frequentive suffix above (-tare), belongs to a group of frequentive suffixes -tare, -(s)sare, and -itare, all derived from the present tense of the verb. See Sihler (2008) for further discussion.

Reduplicated forms of -tare (-titare and -sitare) existed as well, but their origin is more complicated. See note under cantar.
fama f. (Noun) "fame"

10th cent. From Latin fama 'id.' From Proto-Italic *fāma- 'id.' From Proto-Indo-European *bheh2-mh2- "reputation," but originally "speech." From the root *bheh2- "to say." See also habla.

Romance: Western Vulgar Latin: Portugese fama, Catalan fama, French fameux, Italian fameux; Eastern Vulgar Latin: Romanian faimă

Italic: Oscan faamat "orders"

Hellenic: Ancient Greek φήμη (phéme) "speech," Doric φάμα (pháma) 'id.,' Aeolic φάμα (pháma) 'id.'
familia f. (Noun) "family"

13th cent. From Latin familia (legal) "family," but more commonly (and originally) "slave staff." From Proto-Italic *famelias 'id.' A noun formed from an adjective *famelio- "domestic," "of the house," which dates back to a noun in Proto-Indo-European *dhh1-m-elo- "foundation" (see fámulo).

Romance: Western Vulgar Latin: Asturian familia, Portuguese família, Galician familia, Catalan família, French famille, Italian famiglia; Eastern Vulgar Latin: Aromanian fumealji, Romanian familie; Sardinian: famíglia

Italic: Oscan famelos "household," fml "slave," Umbrian fameřias "household," Paelignian famel "slave"

Indo-European: Hellenic: Ancient Greek θεμέλια (themélia) "foundation"
familiar m. (Adjective, Noun) "familiar," "family;" "relative"

15th cent. From Latin familiaris "familiar," but also "pertaining to the household." From familia "household" (see familia) and -aris, an adjective-forming suffix (see -ar (1)).

Romance: Western Vulgar Latin: Portugese familiar, Catalan familiar, French familier, Italian familiare