The hat was found by a member of the public in the area where the last "ping" from Mr Hayez's phone was recorded in the area around the Cape Byron Lighthouse on June 1, AAP understands.

It is being examined to determine if it is relevant to the investigation into the 18-year-old traveller's disappearance, a NSW Police spokeswoman told AAP on Friday.

Mr Hayez was last seen on CCTV walking through the popular seaside town after leaving the Cheeky Monkey's bar about 11pm on May 31.

Staff at the Wake Up! Hostel in Byron Bay found his belongings, including his passport, on June 6, and raised the alarm.

Officers from the local police district as well as the homicide squad, SES volunteers, NSW Surf Lifesaving and the Byron Bay community scoured the area for any trace of him.

The final days of the search focused on the area around the Cape Byron Lighthouse and crews abseiled down the cliffs surrounding the lighthouse in the search for clues.

However, the extensive land, air and sea operation, including dog, foot and aerial searches, failed to locate his clothing or phone, which volunteers believe could be key to learning his fate.

Mr Hayez's parents, Laurent Hayez and Vinciane Delforge, travelled to Australia to help in the search.

Searchers were also joined by officers from the Belgian Federal Police, who supported the investigation in an observer capacity.

NSW Police announced on July 3 that it had suspended their search, although the investigation was continuing.

AAP