A fragment of misty grey film opens this enthralling exhibition. It shows tennis divas in flapper dresses swanning ceremonially round a stadium, and sprinters leaping forwards with greyhound grace beneath the lingering smoke of a starter’s pistol. Swimmers cut through pools like elegant blades.

Cross-country runners hurdle walls then vanish from sight. Two wrestlers lock limbs with such equal force they appear temporarily motionless, still as a statue. And right beside them, as if bodying forth into our space, is their exact counterpart in three dimensions: a cast of an ancient Greek sculpture made thousands of years ago.

Art and reality – the two are so identical as to make you draw breath, and think again about ancient and modern, classical perfectionism and actual reality. Time spools back and forth in the gallery. – timed to coincide with next week’s return of the Olympics to the French capital – is a revelation from first to last.

You soon begin to realise that those Games were a turning point not just for the history of athletics, but for race and class, politics, money and celebrity, and for their expression in modern art. The show fizzes with surprises. Here is Alexander Calder’s lithe wire figure of the American tennis champion Helen Wills balancing on one toe to return a ball, like a sketch in midair, and Diego Rivera’s colossal, heroising pastel of her face.

Here is the steel-ridged football boot of the great Uruguayan wing-half José Andrade, alongs.