You don’t need a test to enter France from the UK if fully vaccinated. Just proof of vaccine. You’ll need to download the French Covid app (which is very good) and upload your vaccine certs from the NHS app to that.
Not sure about Italy, but if you’re entering from France there is no border check as you’re already in the EU.
For return to UK you’ll need an up to date test, passenger locator form and the utter bullshit proof of 2 day test. (Which in essence is just a number entered onto locator form). Be sure to book test in advance, full list on gouv.fr website or via the app.
Personally, when I go to France again in a few weeks I’ll just be making up a number for the return form, nobody checks and the system is not joined up.
Download the ‘Anticovid’ French app and familiarise yourself with it, you’ll need it for hotels, restaurants, bars etc etc as they will need proof from you to scan.
Most pharmacys in towns in France will do an efficient Covid test for travel and provide email results which you upload into the app for €25.