Blandine Staskiewicz, from left, Claire Debono, Bernard Deletré and Pascale Beaudin in rehearsal of Opera Lafayette’s production of Mozart’s “Cosi fan tutte.” (Louis Forget)

Many operagoers wax indignant about supposedly radical stagings of opera. Opera Lafayette’s “Cosi fan tutte,” which opened its weekend run at the Kennedy Center’s Terrace Theater on Friday night, offered compelling proof that a supposedly traditional staging — in this case, with the singers in 18th-century dress — can be the most radical of all.

For Opera Lafayette didn’t change the opera’s setting; it changed the nature of the opera itself. Its thesis: “Cosi” was long among Mozart’s least popular operas, especially in the German-speaking world, because it is fundamentally French at heart. So the conductor and company founder, Ryan Brown, and director Nick Olcott offered “Cosi” as an opera comique — in a French translation, with spoken dialogue in place of Mozart’s sung recitatives and a number of judicious cuts to keep the action moving.

And that’s not all. This production is conceived as part of a double bill (or double-header) that also will include Philidor’s “Les femmes vengées,” an opera comique that Mozart might well have seen when he was in Paris in 1778 — and which has a plot so similar to “Cosi” that Opera Lafayette proposes it as a sequel to Mozart’s opera, with the same singers and characters. (Although the company is based here, Washington, alas, won’t get to experience the double bill as such; the company won’t roll out “Les femmes vengées” until January and won’t present the two operas together until it takes the show on the road later that month, first to New York, then to Versailles, France.)

On paper, it sounds kind of crazy and wildly ambitious. On the stage, this French “Cosi” was nothing short of delightful. It may not be the best-sung or the best-played “Cosi” I’ve heard, but it was hands-down one of the most enjoyable. I wish everyone who loves Mozart had a chance to see it.

Opera Lafayette, of course, specializes in less well-known French opera, and it has parlayed that specialty from its origins in Brown’s Capitol Hill basement some 18 years ago to international recognition (including an impressive catalogue of nine CDs on the Naxos label). One of its hallmarks is the use of period instruments, which here added interest to the familiar score, the chewy textures of the winds giving a new accent to the interleaving solo passages in the overture. Part of Opera Lafayette’s charm is its intimate and sometimes homegrown flavor, which I thought might be a problem in “Cosi.” Yet while it was unusual to hear this music performed by players for whom parts of the score represented an audible challenge, Brown led vigorously, and the whole proved far greater than the sum of its parts. Individual weaknesses or minor mistakes were far less important than the fact that everything added up to such a compelling performance.

I have a preference in any case for hearing Mozart in a small theater; this music is best served by an intimate scale. Opera Lafayette’s cast was largely Canadian, meaning French diction was not a problem, and they all sounded, in the diminutive Terrace Theater, completely respectable: Blandine Staskiewicz as a creamy-voiced Dorabelle, Alex Dobson with a slightly tight but flexible tenor as Guillaume and Antonio Figueroa enjoying clowning around and singing solidly as Fernand. As the maid Delphine (a.k.a. Despina), Claire Debono had a powerful, slightly astringent sound, and Bernard Deletré added a touch of class and gravitas, if some woofiness, as a venerable Don Alphonse.

The soprano Pascale Beaudin best epitomized this production. At first, I thought her voice was simply too small for Fleurdelise/Fiordiligi, but then she found a way to play to her strengths in the second act, singing her aria “Per pieta” (I didn’t document the French translation) with such deliberate quiet elegance and restraint that it was a highlight not just of the evening, but also of my year.

Another of Olcott’s theses is that the relationships between the characters take on credibility in the second act: The two superficial couples find real love only after the two men pretend to go to war, don disguises (in this production, they appeared as French Canadian trappers named Mic and Mac, garbed in leather and furs), and return to woo each other’s girlfriends. This thesis is not unique to Olcott, but he and the cast realized it better than I’ve seen done before. Usually, the second act pales in comparison to the first; here, it gained in dramatic interest until there was considerable suspense, at the end, as to whether the two couples would return to their original configurations. (No spoilers here.)

Opera Lafayette has only recently added full productions, rather than semi-staged ones, to its arsenal, and this production — the second it will take to Versailles — showed that it is gaining in dramatic as well as musical assurance. Olcott and Brown even added a character: a painter, M. Riss, who is engaged to paint the two men’s portrait, and at whose house the action plays out.

Though silent, M. Riss (Jeffrey Thompson) takes an active part in the proceedings, helping Delphine and Alphonse and the two men with their various schemes — and at the end of the opera, Delphine, though outraged at having been duped by everyone, falls ecstatically into his arms. That sets the stage for “Les femmes vengées,” which also will be set in the home of the now-married Riss couple — and in which Thompson will at last find his voice.

“Les femmes vengées” will play at the Terrace Theater on Jan. 17. The double bill of “Cosi fan tutte” and “Les femmes vengées” will play in New York on Jan. 23 and in Versailles on Feb. 1 and 2.