Philippe de Broca's "Dear Detective" is a delightful entertainment, a swift and sparkling blend of romantic comedy and murder mystery. It is likely to become the most popular French movie in the United States since "Cousin, Cousine," and deservedly so.

"Dear Detective," opening today at the Outer Circle 1, is the sort of pick-me-up moviegoers frequently seek and rarely find.

The title refers to the heroine, a dedicated, doughty Parisian police inspector, played by Annie Girardot, who gets her man in both senses of the term. A middle-aged divorcee who resides in the suburbs with her young daughter, her mother and a maternal aunt, Inspector Lise Tanquerelle is hurrying home to celebrate her daughter's birthday when she literally runs into an old acquaintance, Philippe Noiret as Antoine Lemercier. He is a robust but incautious academician who blithely pedals his moped in the path of her car while headed for the Sorbonne, where he teaches Greek.

Within a few minutes Antoine and Lise recognize each other as old college chums who went their separate ways 25 years ago. The reunion puts immediate romantic ideas in the head of Antoine, who has remained a bachelor. Lise feels equally attracted, but she hesitates to reveal her profession to Antoine, since she's learned that it tends to arouse prejudices. Although Antoine is guiltless of the most common prejudice - against women in positions of authority - he is guilty of the next most common - a prejudice against cops, based on the standard liberal intellectual presumption that society could do without them.

Their first date is interrupted when duty summons Lise, who is placed in charge of a murder investigation that rapidly snowballs into a multiple-murder investigation. The scenario by De Broca and Michel Audiard deftly interweaves the circuitous course of the love affair with the circuitous course of the murder case.

Speed was an essential element of the charm that felt so spontaneous and irresistible in De Broca's earliest films, which unfortunately have slipped into obscurity, at least in this country. De Broca's career evolved in a more ponderously whimsical direction with "That Man From Rio" and "King of Hearts."

Now 45, he appears to have caught a second wind, and it propels the scenes in "Dear Detective" along at a breezy, exhilarating pace. De Broca sustains such a bracing tone and rhythm that one can't seriously mind the loopholes or dangling details in the plot.

Girardot and Noiret achieve a prickly but comfortable sexual rapport reminiscent of the chemistry currently displayed by Glenda Jackson and Walter Matthau in the romantic comedy "House Calls." Like Matthau, Noiret is a big, homely physical specimen - tall but stooped, overweight and jowly - who grows more expert as a performer and more appealing as a romantic lead as he ages. Wonderfully deceptive charmers, these actors are making a specialty of projecting sex appeal in shaggy, flabby, rumpled forms.

Girardot, probably an unknown quantity to many American moviegoers since few of her starring vehicles have been imported, embodies Lise with a humorous energy and attractiveness that typify many working women. Obvious as they are, the movies often overlook these qualities, which derive from the fact that women like Lise are too busy and preoccupied to keep up conventional feminine fronts.

De Broca sustains two of the most enjoyable sequences in recent memory. The first is a comic interlude in which Antonine, still ignorant of Lise's profession, launches upon a series of derisive jokes about cops while riding in an unmarked police car sent to pick up Lise. While she does a slow burn, her male colleagues, who treat her with bemused solicitude throughout the story, play it admirably deadpan.

The second is a superlative build-up of suspense at an abandoned factory where the murderer is eventually cornered. Every composition and movement within this fearful setting is charged with wit. De Broca even revives such relics as a creaking door and a headless mannequin with simultaneously creepy and hilarious effectiveness. A shot of Girardot ascending a staircase through a freshly blood-smeared window-pane is a particular pictorial triumph. I haven't felt so thrilled and amused by a scenic murder trap since Audrey Hepburn was being stalked by Matthau at the close of "Charade."

The suspense reaches a natural climax that is then diffused to some extent by stringing out the resolution for perhaps one gratuitous complication too many. However, by this stage one's reservations seem strictly academic. The movie as a whole is a overwhelmingly winning.