You need letters of permission from anyone with parental responsibility
Abduction of children is a thing; international abduction is more serious because legal systems differ between countries, and cross-border enforcement of court orders for child custody and support is extremely difficult. Airlines and a country's exit immigration officers are sometimes very sensitive, and may ask about permission.
Thus, you should carry written statements from both of the child's parents, or the parent who has sole custody and control, identifying the child, and identifying you, and stating that you have permission to take the child from the departure airport and country to a specific destination. Contact details for the parents should be provided to allow quick verification if required. Template letters can be drafted from a reputable legal template.
The rules for Portugal are stricter but otherwise this answer would apply when travelling from UK to any EU country. The French have some rules for French children leaving the territory, but these do not apply to the case above as the family and accompanying minor are British tourists.
If you're asked, and you cannot provide such written evidence, the child (and probably you) won't be allowed to board the flight or whatever means of transport is chosen.