In the Oxford Latin Dictionary (which only covers Classical Latin):
An infant, little child (strictly, one not yet able to talk).
The use of "strictly" in the parenthesis implies that even in Classical Latin the definition wasn't always applied strictly. The dictionary cites two examples from the Corpus Inscriptionum Latinarum:
(used expressly of older children) PASTORINO INFANTI DVLCISSIMO QVI VIX ANN XVII MENS X CIL 10.4802
FL ROMVLIANVS INFAS Q VIXIT AN VI ET M VII 11.1700
Also, in Alfred Ernout and Antoine Meillet's Dictionnaire étymologique de la langue latine:
Comme la période dans laquelle l'enfant est considéré comme incapable de parler finit à sept ans (cf. Quint. 1, 1, 18), on conçoit que infans ait pu désigner l'enfant dans le sens ordinairement réservé à puer. Columelle dit ab infante, Celse ab infantibus dans le sens de a puero, a pueris. De plus, infantes formait couple avec parentes.
Meaning that:
As the period during which the child is considered incapable of speech finishes at the age of seven (cf. Quint. 1, 1, 18), it may be seen that infans was able to designate a child in the sense ordinarily reserved for puer. Columella says ab infante, Celsus ab infantibus in the sense of a puero, a pueris. Moreover, infantes was contrasted with parentes.
In volume I of Le Robert's Dictionnaire historique de la langue française:
En latin classique, infans a designé l'enfant en bas age, puis le jeune enfant; il a remplacé en bas latin puer, puella « enfant de 6 à 14-15 ans » et liberi « les enfants, par rapport aux parents ».
In other words:
In Classical Latin, infans designated a child of a very young age, then later a young child; in Late Latin it replaced puer, puella "child of 6 to 14-15 years of age" and liberi "children in relation to their parents".
