This expression was coined by conservative French essayist Alexandre del Valle, who wrote of "une alliance idéologique ... rouge-brun-vert" in an April 22nd 2002 article in French newspaper Le Figaro, and has more recently used the French phrase "l'axe rouge-vert-brun" in a sense similar to the English usage (see below), with green mainly referring to Islamists, rather than anti-globalists.
Del Valle's conceptual rendering of Islamist ideological trends appears to be based at least partially on even earlier writings in which del Valle himself had charged the United States with creating the "war machine" of "armed Islamism" via its Reagan-era funding of the mujahadeen in Afghanistan.
The later popularity of the "red-green-brown" theory (and its various permutations) derives mainly from a speech given by Roger Cukierman, president of the French Jewish organization CRIF, to a CRIF banquet on January 25th 2003, and given wide circulation by a January 27th/28th 2003 article in the French newspaper Le Monde.
Cukierman used the French term "alliance brun-vert-rouge" to describe the antisemitic alignment supposedly shared by "an extreme right nostalgic for racial hierarchies" (symbolized by the color brown), "an extreme left [which is] anti-globalist, anti-capitalist, anti-American [and] anti-Zionist" (red), and followers of José Bové (green).
In English translation, the phrase "Red-Green-Brown alliance" achieved some minor usage in 2003 among warbloggers and Usenet posters who used it to refer to a perceived convergence in political positions or rhetoric between leftist radicals, Islamists, and the extreme right, so that "green" is generally given a different interpretation than in the original French).
This re-interpretation of the phrase was bolstered by a February 2003 message allegedly from Osama bin Laden, which said "It does not hurt that in the current circumstances, the interests of Muslims coincide with the interests of the socialists in the war against crusaders, taking into account our belief and declaration of the apostasy of the socialists. The socialists and these rulers have lost their credibility of their rule a long time ago and the socialists are infidels wherever they are - whether in Baghdad or Aden [Yemen]".