"Preservation of the plosive sounds /k/ and /ɡ/ before front vowels /e/ and /i/; for example, centum ..."
0: https://en.wikipedia.org/wiki/Palatalization_(sound_change)
Also as a French walking in the street and saying Tuesday and choose day loud in the street, I got a few curious stares :)
In Italian the written letters ce and ci are pronounced with a soft c.
There are plenty of words with a hard c (a k) followed by an e or an i. Italian alphabet doesn't have a k character so those sounds are written as che and chi. That is, in Italian ch is the k sound. Most (all?) of the other languages of the area use ch for a soft c.
To have the hard C in Italian an H needs to be added, CHE or CHI (while in Spanish that leads to something more like tch).