Kevin Chenais and his parents arrived at Penn Station in New York by train from Chicago. They will stay at a hotel in Brooklyn until they catch the Queen Mary 2 for England.
Chenais, 22, has a hormone imbalance and came to the United States from France in 2012 for obesity treatment at the Mayo Clinic in Chicago.
He had planned to fly home in late October but British Airways refused to let him board the plane on the grounds he was too fat.
The family spent more than a week at a hotel near Chicago airport as they tried to resolve the situation.
On Monday they decided to take a train to New York, from where they will sail for England on November 19.
"It is mainly my parents who are angry," he told reporters, looking tired after the 19-hour train trip from Chicago.
His father Rene criticized British Airways for paying just five nights in a hotel, where in the end they spent 13 days. He said the carrier has yet to refund their tickets.
An airline spokesman said the carrier tried to find a solution but in the end it was not possible to tend to Chenais safely.
Chenais needs oxygen constantly and medical oversight, so the week-long trip from New York to Southampton will not be easy.
Chenais has mobility problems and gets around in an electric-powered wheelchair.
As he arrived in New York, with the help of the French consulate, police and staff from the rail company Amtrak helped him off the train and out of the station.
On Tuesday, his father said that two or three days after British Airways refused to let him fly, their travel agent said Air France and Swissair were willing to take him. But the family was out of money.
"We paid $1,200 for the train and then $2,000 for the ship. We cannot pay any more," Rene Chenais said.
He added he was considering legal action against British Airways.
"For now Kevin has to hang in there. We are going to try to visit New York a bit and disconnect," Chenais senior said.
A doctor will examine Chenais in the coming days, and staff on the Queen Mary 2 have been friendly, the father said.