All true except the French do not allow that for a reason to travel to France in fact their latest Government documentation specifically states:
The requirement for pressing grounds does not apply if you are travelling from one of the following countries:
Australia, Israel, Japan, New Zealand, Singapore, South Korea, United Kingdom.
Your trip must however meet one of the exception criteria as listed on the exempted travel certificate and you will be subject to the health control measures below (RT-PCR tests, sworn statement and self-isolation).
So not allowed into France if you are traveling from the UK.