From left to right, First Lady of Ukraine Olena Zelenska, French First Lady Brigitte Macron and Emmanuel Macron during a group photo at a social dinner during the Nato summit in Vilnius. AP

The gruesome find was reported by staff working for President Emmanuel Macron at the beginning of the week, with police called in to investigate, according to the Valeurs Actuelles magazine, which first reported the story.

The fingertip is believed to belong to the sender of the letter who suffers from psychiatric problems, a source close to the investigation told AFP on condition of anonymity.

Between 1,000-1,500 emails and letters are addressed to Macron each day and they are monitored and scanned by a 70-strong team working from offices away from the main Elysee Palace in central Paris.

Macron is known to monitor them as an insight into public opinion and occasionally responds with hand-written messages.

His office declined to comment when contacted by AFP about the finger.