In Classical Latin, "c" was always pronounced as "k". Since Renaissance Latin grammar reform, the correct pronunciation of "c" before "e" or "i" was codified to [ts]. So in Renaissance the true Classical pronunciation must have been forgotten. My question is: when did the pronunciation of "c" before "e" and "i" start to change, and when was this change complete? Did this happen in late or medieval Latin? And in which centuries did these changes take place?
This pronunciation change was underway by the fifth century, but perhaps not finalized until the sixth or seventh.
Paul M. Lloyd, in From Latin to Spanish, writes:
There is no inscriptional evidence of [the palatalization of /k/ and /g/ before the front vowels] until the fifth century, although it may have begun long before, and it continued to be an active process after the Visigoths reached Hispania. (page 137)
In Vox Latina, page 14, W. Sidney Allen indicates evidence for the use of both the [k] and [ts] sounds in the fifth century:
[The hard c] was preserved in words borrowed from Latin by Celtic and Germanic between the first and fifth centuries A. D. [...] It is true that in the course of time a 'softening' took place before e and i [...] but there is no evidence for this before the fifth century A.D.
In Spanish Phonology, page 104, MacPherson writes:
Before the front vowels E and I the tongue position for k was also palatal. [...] By the sixth or seventh century the pronunciation ts, already established in other words, had become standard in this position.
Thus we can suggest a transition period in and around the fifth century, with standardization following in the sixth or seventh.
Sturtevant, The Pronunciation of Greek and Latin, says of the change in pronunciation of C before front vowels (p. 167): "The epigraphical evidence of this change is not abundant enough to inspire confidence before the sixth century". He doesn't discuss the evidence any further, unfortunately.
Note that the change is a little more complicated than just "C became [ts]". The outcomes of Latin C before front vowels in the Romance languages are varied: e.g. French and Portuguese have [s], Italian and Romanian [tʃ] (the sound in "church"), Peninsular Spanish has [θ] (the sound in "thin"), while Sardinian retains [k]. It seems plausible that [ts] was an intermediate stage on the way to the French and Iberian outcomes.
Something similar happened to G before the same vowels: it first became [j], with later specific developments in the daughter languages. Sturtevant thinks the change to [j] occurred by AD 500, so it seems likely that the C change would have taken place at about the same time.