Using your phone abroad is called roaming, to connect to foreign networks you need roaming enabled. Does your phone show a connection to any French networks? If not, your calls, texts & mobile data will be unavailable.
Are you on PAYG or pay-monthly? The process for enabling roaming differs.
PAYG: Your phone is auto-enabled once you have used it in the UK first
Pay-monthly: You need to enable this before leaving the UK, usually by texting ROAMING to 150 from EE's network.
If you've not done whichever applies, this will cause the symptoms you describe. If you're on pay-monthly, you can contact EE CS via another means, and request roaming is activated.
