A joke has long been popular in Europe that if you know three languages, you’re trilingual. If you know two languages, you’re bilingual. If you know just one language, you’re an American.
 
The joke has been cited in print since at least 1983. It’s not known where the joke originated.
 
   
Google Books
The Marine Corps Gazette
Volume 67
1983
Pg. 63:
There is a joke making the rounds in Europe that goes, “A person who knows three languages is called trilingual, and a person who knows two languages is call bilingual, but a person who knows only one language is called an American.
 
23 November 1984, Richmond (VA) Times_Dispatch, “Richard Bland backs language partnerships” by LeeNora Everett, pg. B-5, col. 5:
“A person speaking three languages is called trilingual. A person speaking two languages is bilingual. A person speaking one language—an American.”
(German professor Erika Stronach.—ed.)
 
Google News Archive
18 January 1987, The Sunday Telegraph (Nashua, NH), “Cultural ignorance seen as biggest travel barier” by Catherine Watson (Scripps Howard News Service), pg. H1, col. 1:
Surely you’ve heard the old joke: What do you call a person who speaks three languages? Trilingual. What do you call someone who speaks two languages? Bilingual. And what do you call a person who speaks just one language? American.
   
Google Books
Oral Communications Skills:
A Multicultural Approach
y Lois Scoggins Self and Carol Carlson-Liu
Dubuque, IA: Kendall/Hunt Pub. Co.
1988
Pg. 38:
Europeans sometimes joke that a person fluent in three languages is called “trilingual,” one competent in two languages is “bilingual,” and one who speaks and understands only one language is “American.”
 
Google Books
Bargaining Across Borders:
How to Negotiate Business Successfully Anywhere in the World
By Dean Allen Foster
New York, NY: McGraw-Hill
1992
Pg. 55:
The joke in Europe has long been: “What do you call someone who speaks three languages? Trilingual. What do you call someone who speaks two languages? Bilingual. What do you call someone who speaks one language? An American.
 
Google Books
Practical Argument, (Short Second Edition)
By Laurie G. Kirszner and Stephen R. Mandell
Boston, MA: Bedford/St. Martin’s
2015
Pg. 24:
“What do you call someone who speaks three languages? Trilingual. What do you call someone who speaks two languages? Bilingual. What do you call someone who speaks only one language? American.” As this old joke illustrates, many Americans are unable to communicate in a language other than English.
   
Commentary magazine
Islamists May Win the Language Wars
MICHAEL RUBIN / OCT. 20, 2015
(...)
Meanwhile, language instruction in the United States remains moribund. That old joke — someone who speaks three languages is called “trilingual”; someone who speaks two languages is called “bilingual”; someone who speaks one language is called “American” — still applies.