Dance Reflections, a festival dedicated to choreographic innovation, is not ready to wrap yet: It picks up again next week with a collaboration between the choreographer Dimitri Chamblas and the musician Kim Gordon.

But much has already been presented, providing something that has increasingly been missing in New York in recent years: experimental dance from abroad — in this case, mainly France. Beyond the programs themselves, New York institutions needed this programming boost — artistically and financially. Dance Reflections, produced by Van Cleef & Arpels, is a reminder of a time when festivals routinely brought contemporary dance to the city.

Is it a surprise that a luxury jewelry company is footing the bill? Hardly. In a performing arts world of scarce funding and resources, such support makes sense. And in collaborating with New York venues — among them, the Brooklyn Academy of Music, New York City Center, NYU Skirball — the festival has been a salve.

For the New York iteration of Dance Reflections — the event has also been held in Hong Kong and London — Serge Laurent, Van Cleef & Arpels’s director of dance and culture program, had a plan: to bookend it with influential works of contemporary dance, to show how history leads to inspiration. To start, he chose “Dance,” a 1979 masterpiece with choreography by Lucinda Childs, music by Philip Glass and, originally, a film of the dancers by Sol LeWitt. (The festival will end at the Park Avenue Armory with a re-creation of “The Rite of Spring,” a classic work by Pina Bausch, with dancers from 14 African nations.)

This “Dance,” though, had some problems. Performed by the Lyon Opera Ballet at New York City Center, Oct. 19-21, the restaging featured a 2016 film of its dancers that is identical, according to the program, to LeWitt’s original film featuring Childs and her cast. The LeWitt film, with its larger-than-life dancers, shifts the audience’s perspective, giving way to a dreamlike setting where bodies drift and sail almost angelically. With a different generation, though, the new film was a distraction, taking viewers out of the dance rather than drawing them into its world.

The Lyon experience was flatter, more presentational than lived — and also confusing. It’s not the same “Dance.” Why should it be called such?

The meat of the festival, though, has been the work of a younger generation, especially that of dance artists seldom seen in New York, if at all. Debuts came from Ola Maciejewska, for whom the renegade choreographer Loïe Fuller was a point of departure; and (La)Horde, the spirited dance collective that now leads Ballet National de Marseille. Dorothée Munyaneza, a Rwandan dance artist whose family fled Kigali for London in 1994 after the genocide, brought a work addressing, in part, the memory of violence. The festival also included welcome returns: Boris Charmatz, Rachid Ouramdane and Gisèle Vienne.

At BAM, “Corps Extrêmes,” by Rachid Ouramdane and Compagnie de Chaillot, did double duty: It was part of Dance Reflections, but also one of just seven productions included in BAM’s annual Next Wave Festival. (Programming-wise, this is thin.) Ouramdane’s meditative exploration of extreme sports and acrobatic movement washed over the stage like a balm. It was transporting, not just because of its imagery — a tightrope walker crossing high above the stage, mountain landscapes projected over a white climbing wall, acrobats jumping from shoulders onto that wall — but also because of its plush, gentle atmosphere: sensation as performance.

There were no aggressive thuds from these lithe, floating acrobats. What made the experience even more luminous was the way they landed or ascended into the air, making it almost seem as though the stage was really a cloud. It wasn’t Ouramdane’s most experimental work, but in his dismantling of the conventional rules of time and space, it made you reconsider what experimental could be.

Vienne’s “L’Étang,” a dance-theater adaptation of a short play by the Swiss writer Robert Walser, was one of two presentations at New York Live Arts. It is a blistering example of the choreographer’s controlled, precise slow movement, which warps and stretches time. With formidable performances by Adèle Haenel and Julie Shanahan — they took on multiple roles — Vienne’s exacting pacing was both amazing and excruciating. Like Ouramdane’s “Corps,” it wasn’t conventional dancing. But Vienne’s choreographic precision created sensation; uncomfortable as it was, it broadened the idea of what a dance can be.

In “Mailles,” also at Live Arts, Munyaneza braided the lives and stories of five Black women (African artists or artists of African descent) in order to explore how abandonment leads to feminine freedom and power. As personal stories unfold through music, text, dance and even the performers’ costumes — designed by Stéphanie Coudert — a collective memory builds through a choir of sound and movement. As mesmerizing as the performers were (none as vivid as Nido Uwera), the threads of their stories had trouble binding together as one.

At the French Institute Alliance Française, Maciejewska highlighted three performers — and loads of fabric — in “Bombyx Mori” to draw a connection between the silkworm and Fuller’s “Serpentine Dance” (1892), which incorporated lights and billowing fabric to transform a dancer into a human butterfly. The link between the silkworm and the dance was a little dubious, but visually and sonically “Bombyx” had its moments — especially when microphones dangling from the ceiling picked up the sound of the rustling fabric manipulated by the trio with curving swoops of the arms.

Charmatz performed a solo, “Somnole,” which explored the moment just before sleep overcomes a body. Set to whistling renditions of music including “Summertime” and “The Pink Panther” — performed by Charmatz himself as his ever-drifting body wavered between drowsiness and alertness — the solo was intended to impart, as he wrote on his website, “the undertow of daydreams and the scream of awakening.”

While it achieved that to an extent, what it looked and sounded like was not so enticing: noisy mime. But Charmatz is a beautiful, generous dancer whose presence was a reminder of France Moves, a festival that feels like the unofficial precursor to Dance Reflections. That festival, which arrived in New York in 2001, served as an introduction to Charmatz, then the youngest and most intriguing choreographer on the lineup. His “herses (une lente introduction),” with a nude cast, took place at the Kitchen, a theater that rarely presents dance at all these days. It used to be a force.

Charmatz, now the director of Tanztheater Wuppertal Pina Bausch, has himself grown into a force in contemporary dance. And (La)Horde — at least judging by Dance Reflections — is on that route, too. Its “Room With a View,” a collaboration with the composer Rone, moved from violence to peace with decisive attack and crystalline tenderness, but the group’s mixed bill, featuring works by Childs, Lasseindra Ninja and the collective, was even more of an indication of how wide its creative lens is.

(La)Horde presented two excerpts from an evening-length work, “Age of Content,” including “Tik Tok Jazz,” a galvanizing piece set to music by Glass that takes inspiration from Childs’s rigid use of geometric structure as it layers gestures from viral TikTok dances at rapid-fire speed. It was a spectacular moment that revealed (La)Horde’s ability to merge history with the present day. Beyond its work with fashion, music — and Madonna — dance is at the heart of its mission.

The collective knows dance is fragile and wants to protect it. (La)Horde often repeats a version of a saying: “We need to blow on the embers to keep the flame alive.” So far, the festival has given it a decent glow.