There are at least two stories on the theme of "the letter in French (or some language) that no one will translate"; maybe one or the other is the one you remember reading.
I. The older one (from 1896) is "The Mysterious Card" together with its sequel "The Mysterious Card Unveiled" by Cleveland Moffett. Opinion is divided as to whether the sequel redeems or ruins the original story. The stories are in the anthology Masterpieces of Mystery: Riddle Stories, edited by Joseph Lewis French, which is available at Project Gutenberg. The following summary is from a review of the Mysterious Card series in Prashant C. Trikannad's blog Chess, Comics, Crosswords, Books, Music, Cinema:
In The Mysterious Card, Richard Burwell is visiting Paris on business while his wife and daughter are vacationing in London. Bored and lonely, the unassuming gentleman goes to the Folies Bergëre, a cabaret music hall, and is sitting in its garden when a mysterious woman accompanied by a tall distinguished man with glasses leaves a card on his table and walks away.
The card bears some French words written in purple ink. Since Burwell does not know the language, he decides to find out their meaning and gets the biggest shock of his life. The people he shows the card to are so repulsed by what they see that they want nothing to do with him. Hotel managers and proprietors throw him out, his wife labels him a monster and disowns him, and his closest friends desert him. The French police arrest him but the American Legation (diplomatic mission) in Paris bails him out with the condition that he leaves the country within 24 hours.
Burwell returns to New York, angry, confused, anxious, humiliated, and dejected, as his frantic quest to unravel the secrets of the card ends in a manner he wouldn't have thought his entire life.
Then, one day, Burwell sees the mysterious lady in a carriage on Broadway. After many attempts he succeeds in meeting her at her house and finds out that she is ailing and dying. She recognises him and murmurs, “I gave you the card because I wanted you to . . . to . . .”
As I said, the two stories are only 31 pages long and I’m not going to spoil it for those of you who haven’t read them, which means I can tell you very little of what happens in the sequel.
The events in The Mysterious Card Unveiled take place 11 years after Richard Burwell returns home. It is a first-person account by a kind and scrupulous physician who is treating him for mental disorder and unspecific ailments. He is actually looking for someone to talk to, someone he can unburden himself on. The doctor, an enthusiastic student of palmistry, takes a keen interest in Burwell when he discovers on his patient’s palm a sinister double circle on Saturn's mount, with the cross inside, “a marking so rare as to portend some stupendous destiny of good or evil, more probably the latter.”
Much happens from this point to the end of the story, which is actually a flashback as the tall man with the glasses approaches the physician to explain everything from the beginning until the time his sister, the mysterious lady, dropped the card in front of Burwell. The woman, with a passion for the occult, had discovered that he was possessed by the demon, “a kulos-man, a fiend-soul,” as she called him, and was responsible for murders and mutilations and other unthinkable crimes.
The secret of the mysterious white card—the cursed life of the wealthy and philanthropic Richard Burwell—is revealed in the end, though, in an unexpected way.
II. The newer one (from 1937) is "The Most Maddening Story in the World" by Ralph Straus, available at Project Gutenberg of Australia. In this story, the monolingual protagonist gets the mysterious card not from a mysterious woman but from a seemingly friendly French comte, and the writing is in an unknown language:
"He took out of his card-case a blank card—exactly similar, I mean, to an ordinary visiting card, but quite plain. Then he scribbled a few words on it, and handed it over.
"'If you should go to any of the hotels I've mentioned,' said he, 'this may be of use. Often a stranger is not given the most comfortable room.'
"Brassington thanked him and looked at the writing. He did not recognize the language, although he was convinced that it was neither French nor German. It did not seem to be Italian or Spanish, but, as Brassington told me afterwards, he thought, without knowing why, that it might be Russian."
Of course the card does not help at all; quite the contrary, everyone who sees it is angry and disgusted. He learns to stop showing it, but in Prague the police demand to see the card; when he refuses, they search him and find it, and lock him up in a dungeon. After he gets out of Austria, he meets a polite Greek gentleman in Italy, who reads the card and stabs him. Finally he gets back to England, sees a neurologist, tells his story, and then shows him the card:
"The doctor took it up and examined it carefully. He turned it over and held it up to the light.
"Then he smiled. 'Exactly what I expected to find,' he said.
"'You mean. . . . I. . . .' Brassington sat down and stared at him. 'I don't understand. . . .'
"'There is nothing on the card,' said Dr. Aylmer. 'Both sides are quite blank.'"
"But," I exclaimed, "I don't understand either. There must have been something. . . ."
"I told you," said John Chester, "that this was the most maddening story in the world, and you mustn't ask me any more questions. I can only tell you that when the doctor saw the card it was blank, but whether it had always been blank—Hullo, the old General has obtained his drink! Waiter, you may bring us two whiskies-and-sodas."
End of story. No explanation, no sequel as far as I know.