traveling with a minor

My 16 year old niece will be visiting me this summer. We plan to take the train to Paris for a weekend and to London for a weekend. She will be traveling on her US passport and I will be traveling on my passport. Her last name and my last name are not the same (she is my sister's child). Does anyone know if there will be any issues with our traveling together without any of her parents? Who should I contact to ask--the UK embassy for London but for France there should be no border control so don't know who to ask. I have been on the train to Paris when police have come around and asked for passports and tickets so I want to be prepared with whatever documentation I might need to prove I am not kidnapping her and that she is authorized to travel with me. I have asked my sister to send a signed letter authorizing the travel but not sure if it needs to be more "official." Thanks for any advice.