Instead of the Cervantes' classic he had known from childhood - his Spanish grandmother had read it to him, as a dire warning against delusions of grandeur - Montalvo looked to the Petipa ballet of 1869. He even had his dancers coached in the choreography by Carole Arbo, a former principal ballerina at the Paris Opera Ballet. But, typically, his Don Quichotte de Trocadero does not follow in the exact footsteps of that classic either.
Montalvo is the man behind that "elephant walking on a tightrope" image that graced the front cover of the EIF brochure in 2007. That eye-catching illusion was part of his quirky video work for On Danse, a blissful melange of live dance - all sorts, from hip hop to pointe-work - interacting with fantastical on-screen footage. And all set to Rameau.
Counterpointing the rhythms and textures of 18th century music with brilliantly whimsical video and hot, adorable dance was like a palate-cleanser: as your eye soaked up one stream of information and your ear tuned into another, the effect was of looking and listening with a fresh, you could say almost innocent, intensity. There was no room for a deadening sense of familiarity, as nothing in On Danse was quite what audiences expected.
The same is likely to be true of the work that rounds off the dance strand in this year's Edinburgh International Festival. The title is the first clue to Montalvo's idiosyncratic take on a well-worn tale. His Don Quixote is no longer in La Mancha. He is in the Paris Metro. Trocadero is the station nearest to the Theatre National de Chaillot where Montalvo is artistic director.
Like his Don Q, Montalvo has descended into its underground culture, into the swirling masses of fellow-travellers and glimpsed moments of other people's lives and relationships being played out against a backdrop-blitz of advertisements selling hopes of a 'better you' .
"I think there is a little bit of Don Quichotte in everyone," he says. "That need to dream and escape the life we have. Travelling on the underground, when we look out of the window, it is easy to feel that mood. This old man, my Don Quichotte, is that kind of dreamer on the Paris underground."
On stage, that character is embodied in Patrice Thibaud, one of France's foremost comedy actors and no stranger to Edinburgh. In 2009, Thibaud, along with pianist Phillippe Leygnac, won a Herald Angel award for a wickedly funny Fringe show called Cocorico. In it, the Laurel and Hardy sight gag of big guy/little guy against the world - with Leygnac a deadpan Stan to Thibaud's expansive Oliver (without the waistcoat-stretching paunch, however) - became a celebration of mime as the universal language of comedy.
Montalvo's voice alone conveys his enthusiasm for Thibaud and his remarkable talents.
"I would not have done this piece without Patrice Thibaud," he says. "I needed a Don Quichotte who could evoke the whole realm of burlesque - not in the English sense of burlesque, but in the film-comedy manner of a Chaplin. Bringing humour to dance is always tricky, but Patrice is able to do that. He is not a dancer, but the way his body moves brings not just the humour I wanted, but also the sadness. A sadness we can all feel."
There is a pause. Laughing, he adds "There is a saying 'at 20, we go to sleep as Don Quichotte, and at 40 we wake up as Sancho Panza!' and it's true. We maybe lose hope. For me, this show is about the dreams that still live in an old man's head. And it's about dance itself, and the Petipa ballet especially. Because for me, dance is a happiness that I want to create for myself, as well as for others."
For Thibaud, however, dance was an unknown territory, and a scary one at that. Walking into the rehearsal studio for the first time he felt "a concern that I would not be able to do any of it - but at the same time, I was very intrigued by it. I am curious about other art forms, anyway. I have had a go at different things before - not just comedy but tragedy, opera, music - but never dance.
"Then I realised, it was not really a matter of movement technique as such. The important thing was the rhythm, and the energy of it. I already work a lot with music, and there was something about the Minkus score for Don Quixote I felt very comfortable with - it has a happy, interestingly varied flow that, as a physical theatre actor, I loved responding to. My character, maybe, is a choreographer himself - or perhaps that was his unfulfilled ambition. But he knows about Petipa's ballet, about the Cervantes novel, and on the underground he turns his own daily journey into a kind of imagined dance that comes alive. He looks about him, and what he sees gets transformed."
Illusions become reality and vice versa here. The past is translated into our everyday present, because - as Montalvo reminds us - human nature does not really change over centuries, even if our ideals and aspirations acquire a modern gloss.
And Petipa's choreography is acknowledged and embraced by the thrillingly different styles Montalvo's dancers bring to the mix, just as Petipa himself brought elements of flamenco and popular folk dance into his classical ballet structures.
Yet again, Montalvo rewrites the book on how dance can reach out and touch us - his Don Quichotte de Trocadero tilts at the windmills of convention. See it, and dream on.
Don Quichotte de Trocadero is at Edinburgh's Festival Theatre tonight until Saturday