Momentous and monumental, Anish Kapoor's "Leviathan" has opened its air-lock doors at the Grand Palais, following weeks-long gushing by the media and art-world stakeholders. As the first visitors shuffled through the darkened space of the work's revolving doors and entered the immense vermilion "womb," the verdict already seemed to be in on the Indian-born British artist's carefully kept secret. "As if the Grand Palais is pregnant," wrote Les Echos, while Libération called it a "fascinating, delicious echo chamber." There has been talk of infinity, the belly of a whale or beast, a cathedral and Kapoor's own "wow," exclaimed when he finally saw the finished work.

"Leviathan" is something of a master project for the world-renowned sculptor, even out-sizing immense works like the trumpet-style "Marsyas" that filled the Tate Modern's Turbine Hall in 2002-2003. "Leviathan" exists as three linked spheres that stretch 35 yards into the air, which you can enter and walk around inside. The project has, from inception, been huge. Leviathan was, over the past two years, engineered in Britain and designed in Italy, while Kapoor turned to French textile manufacturers Serge Ferrari (who also worked on "Marsyas") to create the uniquely tinted and light-sensitive fabric that has now been painstakingly inflated to fill more than half of the Grand Palais. (Importantly, Kapoor has also dedicated the high-profile work to imprisoned Chinese artist Ai Weiwei, as a gesture of solidarity.)

After Christian Boltanski's pile of clothing in 2010, Richard Serra's pillars in 2008, and Anselm Kiefer's stream of demolished buildings in 2007, "Leviathan" is the first work that truly fulfills the implied promise of "Monumenta." "I feel like I've been working on this work for, certainly, the last 20 years and perhaps the challenge of this building allowed a certain kind of awakening," Kapoor told a throng of reporters following him in and out of "Leviathan" at the press opening on Tuesday. He described the work as a "big beast that is inarticulate, yet has great beauty."

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Overwhelming on paper, "Leviathan" is nevertheless sensorially underwhelming. When one enters into the giant balloon-like sphere structures and gets past the darkness of the blackened doorway, Kapoor reprises his ever-beloved color red, but in a shade that relies on the shifting daylight of the Grand Palais to come to life. In bright sunlight, the shadow patterns of the vaulted glass nave are imprinted onto the red canvas. Visit on a clouded day and you will only see a pale reddish haze. The texture of "Leviathan"'s innards likewise veers from a rubber-like appearance to the illusion of a parquet finish.

The effect is mildly claustrophobic and far less awe-inspiring than expected. Visitors are confined to the first of three chambers and the fabric curves steeply up and around to block any would-be climbers from peeking into the undiscovered orb-chambers that it connects to. There is a hint of thwarted exploration, of denied space, but the emotion remains unexplored, almost suffocated by the blanket of dim, monochrome red.

"Leviathan" could be meditative if it succeeded in either stimulating a particular sense — or depriving us of them all. Frustratingly, the work falls somewhere in the middle, tamely starting something it refuses to finish. Whether you feel off-balance, contemplative or anything else will likely depend on whether you believe the hype around the artwork and have tricked your mind into acting in accordance with expectations. Inside "Leviathan," little is offered.

The void of impression could be a goal in itself. Kapoor has pitched Leviathan as a "cathedral of the body," and cathedrals are mostly places of quiet worship. The artist has also suggested that this "monster burdened with its corpse ... stands guard over some forgotten regions of our conscience." "Leviathan" could then be an extension of personal space, but the work seems to stifle this, cocooning you in numbness — and leaving whichever soul-searching you may do to be invaded and interrupted by up to 270 other visitors.

The second half of the experience comes when walking around the exterior of the immense spheres, and underneath their inaccessible corridors of connected membrane, offering a full view of the work that has barely squeezed into the Grand Palais and mimics the venue's three-point, clover-like plan. The sight is impressive and the venue, with its classic industrial-deco details, lends itself well to the installation. But its interrogation of full and empty space is again preempted by the simplicity and lack of intent in the design — wherever you go, "Leviathan" remains a big balloon. There is a sense of missed opportunity when it comes to any juxtaposition of the inner self and the outer self that could be mirrored in the two different experiences of "Leviathan." Without an inner part, the necessary action-reaction cannot materialize.

The suggestion of some kind of statement about an equilibrium between presence and absence is the closest Kapoor comes to a statement with "Leviathan" — but the final destination is an uncomfortable nothingness. As a celebration of transitory moments or a trigger to investigate personal hidden worlds, the experience is not particularly gripping. "Leviathan" is not quite a big disappointment, at least not as big as the work itself — but unless you are particularly excited about the thought of walking around inside a giant rubber bouncy ball, you won't be amazed by this work.

Anish Kapoor's "Leviathan" at Paris's Grand Palais: