To elaborate unnecessarily, frāter can securely be traced back to PIE *bʰréh₂tēr, which is a combination of the root *bʰréh₂ + a suffix *-ter (+ the nominative singular ending *-s, which is lost with compensatory lengthening of the *-e- in the suffix, as per Szemerényi's law). That suffix, or at the very least one that looks exactly like it, is also seen in other kinship terms like *ph₂tḗr > L pater, G πατήρ, E father; *méh₂tēr > L māter, G μήτηρ, E mother; *dʰugh₂tḗr > G θυγάτηρ, E daughter (no surviving reflex in Latin, but there's an attested dative singular futír in Oscan, another Italic language).
What the *bʰréh₂- part means actually isn't clear; Pinault constructs an etymology *bʰr-éh₂- 'group of males borne by the same mother', which would make it a compound rather than a root and combines the root *bʰer- 'to bear' (also seen in L ferre) in the zero-grade with a collective/abstract suffix *-eh₂ (later *-a; this is the same suffix that may have given rise to the feminine in late PIE, later seen in the Latin and Greek first declension). He consequently also identifies the *-ter- as a contrastive suffix, rather than what is usually called an agentive suffix in *ph₂tḗr, where the *ph₂- part is then taken to be the zero-grade of *peh₂- 'to protect, shepherd' (also reflected e.g. in L pascere) (though it may also just be a nursery word, as is likely the case for the *méh₂- in *méh₂tēr). Certain details continue to be up for debate, but the important thing is that PIE *bʰréh₂tēr has descendants in so many languages (not just Latin, Greek, and English) that neither its age nor its reconstructed shape, including the initial *bʰ, are in serious question.
Fere, on the other hand, is reconstructed with an initial *dʰ, which also developed into f in Latin at the start of words: it's cognate with firmus and built on the root *dʰer- 'to hold' (semantically the development was 'holding' > 'close by' > 'approximately, nearly'; unfortunately besides Latin that root only seems to have unambiguous reflexes in Indo-Iranian and Baltic languages, but it may be that G θρᾶνος 'supporting beam' is one). It cannot have contributed to *bʰréh₂tēr.
Alter does not mean 'another', it means 'the other (of two)', and its -ter clearly is the contrastive suffix mentioned earlier (which is also seen e.g. in Greek comparatives). Neither alter itself nor its reconstructed PIE etymon *h₂él-ter- will have contributed to the word at any stage, but as said, the suffix might be the same. It might also be the homonymous but distinct agentive suffix, or it may be fully meaningless in *bʰréh₂tēr and only exist by analogy with the other kinship terms. We don't know.
Fructus, finally, is from the verb fruor < Proto-Italic *frugjor < PIE *bʰruHg-ye-ti (where the H represents some laryngeal; we can't tell which). Its root *bʰreu̯Hg- 'to make use of' has reflexes (also in the zero-grade) in English to brook, Dutch gebruiken 'to use'. Like *bʰréh₂- it starts with *bʰr, but the rest of it precludes it from having gone into *bʰréh₂tēr; PIE likes building on roots, but it does not split them.
It's generally safe to assume any etymology proposed before the 19th century is false.
(Source for reconstructions is mainly De Vaan's Etymological Dictionary of Latin and the other Italic Languages.)