Travel with teenager to EU

[GitsandShigggles]

I'm trying to figure out the 'current' rules for travel with a 16yo to Italy via France, appreciate that by the time I travel in January the rules may have changed.
Son is 16 and single vaccinated with the Pfizer vax, there isn't currently an option as far as I can tell for him to get a second jab. Having searched and searched, the terminology used for entry to a EU country is 'fully vaccinated' which would mean no need for PCR test for entry. However as my son has only had a single jab he's not considered fully vaccinated and needs a private PCR test.
Looking for advice from anyone who can confirm or correct me, any suggestions for trying to get a second vax for them if necessary. TIA

This is exactly how we have interpreted the information.

@frozendaisy

This is exactly how we have interpreted the information.

Thanks. Not the end of the world but logistically may prove challenging as we travel on 2nd Jan and need a PCR from 24 hours previously which I don't expect will be simple on New Years Day.

He also (currently) would need to quarantine for 5 days as he's over 12

Sorry, scrap that (but do check the Italian websites as well, as they seem to contradict)
Gov UK says under 18s travelling with vaccinated adult doesn't need to quarantine, Italian gov website just gives a blanket fully vaccinated + neg test- no quarantine. Not fully vaccinated + neg test- 5 days quarantine. Doesn't mention ages.

Just seen you're entering from France so list C for Italy with only test required. It will have to be every 48 hours though to use transport, eat inside, visit museums etc.

Things may have changed by then of course!