An architecture firm has proposed replacing the roof of Notre Dame Cathedral with a swimming pool, as France prepares to launch an international competition to restore the fire-damaged gothic edifice to its former glory.

After the roof and spire of Notre Dame were damaged in a fire watched worldwide in April, the French president, Emmanuel Macron, said he was open to a “contemporary gesture” in rebuilding it “more beautiful than before”, and the prime Minister, Edouard Philippe, called for a new spire “adapted to the techniques and the challenges of our era”.

The ideas aired publicly so far are unlikely to please traditionalists who want the 12th century gothic cathedral complete with 19th century spire by Eugène Viollet-le-Duc put back the way it was.

One week after the 15 April fire, the French firm Studio NAB proposed a giant greenhouse roof; others have suggested a park or terrace or even forest along with a plain or stained-glass or metal spire. The British architect Norman Foster suggested the new spire should be “contemporary and very spiritual.” Some say it should not be rebuilt at all but given an ephemeral spire made of beams of light.

“We’re not obliged to rebuild identically,” said the architect Alexandre Chassang, who has designed a proposal for a glass spire.

Stockholm-based Ulf Mejergren Architects (UMA) has drawn up plans for a cross-shaped pool covering the entire roof area, watched over by the statues of the 12 apostles that escaped the inferno as they had been removed for restoration.

“A cathedral is in our opinion not an isolated island in the urban fabric; it belongs to the city and to the people,” UMA added.

As Twitter users had fun with their own, most often bizarre, ideas, heritage experts urged caution.

Florian Renucci, a master mason at the experimental medieval building site at Guédelon in Burgundy, believes Notre Dame should be – and can be – restored as it was.

“The restoration of Notre Dame should respect the techniques of the era in which it was built, with respect for the overall gothic harmony that comes from a combination of the humans who built it and the materials they used, stone, wood, iron and glass,” Renucci said. “We must respect the spirit of the that work. The gothic period was a high point in architecture … if we do it right it will last another 1,000 years.”