The family of a French teenager who mysteriously disappeared in Piha two months ago say he was likely going to collect the area's famed black sand to take home to show them.

But they say he was also lonely and "quite disturbed" before he went missing and had suffered several "sentimental setbacks" during his time in New Zealand.

Eloi Jean Rolland, 18, came to Auckland in September to study English.

Eloi Rolland in Auckland in March this year. Photo / Supplied

He was staying with a host family in Birkenhead on the North Shore and was reported missing after he failed to return home on March 6.

Police would later confirm that at 6.30am that day the teen was captured on CCTV footage catching a train from Britomart Station in the CBD.

Then at 7.26am he exited Fruitvale Station at New Lynn.

Cellphone data picked up later placed the teenager in the area of Piha Rd at 9.18am.

Police believe he may have walked there - a journey of at least 10km.

Eloi Jean Rolland, 18, captured on CCTV at the Britomart train station in downtown Auckland on Saturday, March 7.

Rolland has not been seen since and his phone stopped transmitting soon after that last location was picked up.

A T-shirt found last month at Karekare - an area 7.3km south of Piha - is being forensically tested to determine if it belongs to Rolland.

Officers searched the area extensively but to date, there has been no sign of Rolland.

Today the Herald spoke to Rolland's sister Aurore Allogho-Boundzanga who said he was in regular contact with her and the rest of the family.

They spoke or messaged several times a week.

"He was determined to want to return to France as quickly as possible, explaining to everyone that he was homesick," she said.

"I told him of my surprise at this premature return which seemed to me very abnormally hasty."

Rolland's return ticket was scheduled for late May but he was set to head back to Montpelier in Southern France, on May 21.

"He assured me that he wanted to see his missing friends again, that he felt too lonely and that he preferred to return as soon as possible to prepare for a test in view of joining the Air Force," Allogho-Boundzanga said.

Police believe missing teen Eloi Rolland may have walked from the train station in New Lynn to the vicinity of Piha Road, near Scenic Drive, on Saturday, March 7.

"If he failed, he planned to continue his studies in a preparatory class in Toulouse."

She said her brother had suffered "several sentimental disappointments" but seemed to be "resilient" when they last spoke.

He wanted to move on and "accept things as they were".

"He had positive thoughts. He really looked forward to coming back.

"He expressed the desire to return to France as quickly as possible, justifying this by a heavy loneliness and projects to be carried out."

Allogho-Boundzanga said her family had spent endless hours speculating about what may have happened to Rolland.

But they really had no idea.

"We were not by his side in New Zealand, we only knew what he wanted to tell us, both about his schedule and his friends, his outings, his activities, his moods," she told the Herald.

"Personally, I found him quite disturbed in the last months preceding his disappearance.

"I had questioned him at length on this subject and yet he kept assuring me that everything was fine and that there was no reason to worry.

"So suicide? An accident? A bad meeting? A settlement of accounts? Since March 6, the question remains completely in suspense."

Rolland's family wanted to come to New Zealand and look for him themselves, but the global Covid-19 pandemic and travel restrictions meant that was not possible.

Allogho-Boundzanga said she felt "impotence" at not being able to "actively participate" in the investigation.

"It is very difficult for all of us, especially my parents," she said.

"Leaving your child alone and as far away [as Auckland] is not trivial and they had thought about it a long time before agreeing to support Eloi in this project which was dear to their heart.

"They were afraid for him, like any parent, for fear that misfortune could happen to their child.

"They did not want to bully him in his dreams and made sure to maintain the safest possible environment around him, despite the distance."

Eloi Rolland was enjoying his time in Auckland where he was studying English. Photo / Supplied

She said everything about the trip was well organised and her parents regularly sent money and were "vigilant from afar" to make sure he lacked for nothing.

Her parents had been in contact with the host family, who reported Rolland missing "very quickly".

No one knew where Rolland had been the night before or who he was with.

"He had talked about going to Piha on foot to fetch and bring back sand from New Zealand as a souvenir of his trip," said his sister.

"He had informed our parents of his intention to go there on foot in the morning and also to return on foot in the afternoon, but without specifying the date on which he planned to make this excursion."

Allogho-Boundzanga said her brother was enjoying New Zealand.

His main reason for being here was to learn English but he also worked part-time in a restaurant and then in a hotel.

"He participated in organised evenings when the opportunity arose, for fun, but also in search of love," she said

"Since January, he expressed an interest first of all in psychology then he became very suddenly and strongly interested in the environmental cause.

"He also found a very recent attraction for hiking, it seems.

"He sometimes spoke to me about Piha saying that it was a wonderful place. He even wanted to bring us [the family] to New Zealand just so we could see the beauty of this beach."

Rolland's sister said he was a calm and kind teenager who was "a bit dreamy and sometimes naive".

"He is passionate about sailing, especially catamaran. He likes travelling," she said.

"We thank all the efforts undertaken to find Eloi, and we are very grateful for the responsiveness, the benevolence of the police of New Zealand and all the inhabitants."

Rolland has two Facebook pages which he regularly updated.

On March 6 he made his last post, an image of a black square.

He listed popular Viaduct bar Headquarters and Suppremo Hospitality Solutions - a company that provides event staff - as places he worked.

Detective Senior Sergeant Callum McNeill said police were keeping an open mind around what has happened to Rolland.

"But as each day passes, the chances of finding Eloi alive and well are sadly becoming more slim," he said.

"This has been an incredibly difficult time for his family in France and we are supporting them as best we can.

"We continue to do everything we can to find Eloi and provide his family with answers to the questions they desperately seek."