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At the Pentagon in Washington, D.C., Colonel Leland gathers a group of psychologists, including Lieutenant Vicki Loren, to brief them on the situation at the Army’s Arctic radar station, where 104 men have been stationed for seven months.  Although the Army assumed bachelors would be better equipped to handle the isolated outpost than married men, the soldiers are “restless,” manifesting their discomfort in bursts of violence, negligence and disrespect.

When Leland asks the psychologists for advice about how to take the men's minds off women, Vicki suggests that they be allowed to choose their perfect furlough.  The men will then select one of their group to go on the trip, and the others will be so identified with this man that they will all live vicariously through him, thus breaking the tension.  In the Arctic, the sluggish men are, indeed, infused with energy by this assignment, and at the urging of Corporal Paul Hodges, suggest a three-week trip to Paris in the company of Argentinean movie star Sandra Roca.

Although Leland is annoyed that the men did not choose a more staid vacation, and Sandra initially does not want to leave America, her manager, Harvey Franklin, launches a huge press campaign, and the positive publicity convinces everyone to go along with the plan.  Sandra is to draw the winning number out of a hat, and even though Paul hoodwinks half his fellow soldiers into giving them his numbers, a mild-mannered man wins the draw.  The man's laryngitis prevents anyone but Paul from hearing that he has won, and Paul is quickly able persuade him that his fiancée would not take kindly to his trip, which must live up to the expectations of every man on base.  Paul comes forward with the winning number, but when Leland discovers the corporal’s history of womanizing, he angrily insists that Vicki and Major Collins chaperone the couple in Paris.

Paul and Sandra meet and are instantly attracted to each other, and on the plane sleep in adjacent berths.  Sandra’s broken window sash prompts Paul to suggest that they switch berths, but in the morning Vicki and Collins mistakenly assume that they have spent the night together, and redouble their efforts to keep them apart.  To that end, Paul is stationed on a different floor of their Paris hotel, with two M.P.s guarding him constantly.  Over the next few days, Paul and Sandra are accompanied everywhere by an entourage, watched over by Vicki and Sandra’s publicist, Liz Baker.

One night at a club, when Vicki instructs Paul to write postcards to the soldiers while Sandra dances with Collins, a frustrated Paul offends Vicki by suggesting that her severity is unnatural and frigid.  Later, he fashions a rope out of sheets and climbs through Sandra’s window, only to find Vicki standing guard.  Desperate, Paul then calls a bellboy to his room, steals his uniform, and marches out of his room undetected.  In the hall, however, he is spotted by a manager, who instructs him in French to change a lightbulb.  Not understanding the language, Paul blunders through the room until he is finally identified.

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After two weeks without a moment alone, Paul pleads with Vicki for permission to take a walk, and although she agrees, she rushes out after him.  He finally evades her at a café, and by the time she returns to the hotel, he has already spirited Sandra away on a picnic.  There, the tipsy starlet announces that she is secretly married to a publicist, prompting the now gentlemanly Paul to toast to their happiness.  On the way back to the hotel, they run out of gas, and are helped by Henri Valentin and his son Rene.  They bring the couple to their winery, where Sandra falls into the vat of grapes and consequently returns to the hotel not only drunk but soaking wet.  Although Paul insists their outing was innocent, Vicki, whose excessive worry has prompted Liz to diagnose her as lovesick, refuses to believe him.  He is so incensed him that he drags her to the Valentins'.

While corroborating Paul's story, they knock Vicki into the vat, and she is forced to stay for dinner waiting for her clothes to dry.  Vicki transforms a bed sheet into a fetching gown, prompting Paul to see her in a new light, and after dinner his sincere compliments inspire her to kiss him.  They return to the hotel, where Paul retires to his room and Vicki joins Collins and Liz in the ailing Sandra’s room.  After the doctor announces that Sandra not only has a cold but is also pregnant, everyone assumes that the baby is Paul’s.  When they confront Sandra, she mistakenly believes they know about her marriage and cheerfully informs them that Paul just wants to be friends.

While Vicki orders Paul, who denies that the baby is his, to be confined to his quarters, Leland and Harvey fly to Paris, where Harvey plans for Paul and Sandra to marry.  Liz tells Paul that Vicki is leaving town, prompting him to elude the M.P.s and chase her to the airport.  After a long pursuit, however, Vicki still refuses to believe Paul, and he leaves in anger.  Their taxi driver assumes Paul has gotten both Sandra and Vicki pregnant and spreads this news throughout the hotel, inspiring the hotel bartender to treat Paul to free drinks.  When the doctor, returning to check on Sandra, hears the rumor and announces it to Leland and the group, the Colonel orders Vicki be brought back to the hotel.  Once she is there, Harvey finds Paul and drags him to Sandra’s room, where a confused Sandra reveals her marriage to everyone.  Paul asks to be allowed to return to the base, and Vicki, ashamed of her suspicions, lies to Leland that she is pregnant in order to force Paul to marry her.  Although Paul pretends to remain angry, he is delighted with the arrangement.

Back at the Arctic base, the soldiers watch the newsreel of Paul and Vicki’s wedding, thrilled to see what a great time they have had on their furlough.