What does it mean by "Un coup de rouge" in this context?

Most likely, this is a pun based on the po­lit­i­cal mean­ing of the word coup and the as­so­ci­a­tion be­tween the the color red and left-lean­ing Euro­pean pol­i­tics like those of com­mu­nism and so­cial­ism.

Orig­i­nat­ing from the French ex­pres­sion coup d’é­tat, which can per Dic­tionary.com be de­fined as

a sud­den and de­ci­sive ac­tion in pol­i­tics, es­pe­cially one re­sult­ing in a change of gov­ern­ment il­le­gally or by force.

Wiki­pedia ob­serves that in pol­i­tics, the color red is of­ten as­so­ci­ated with the far-left — ex­cept in the United States this mil­len­nium, where it has come to be as­so­ci­ated with the far-right in­stead.

So the author made a sub­tle joke, us­ing two po­lit­i­cal words to­gether to form a pun.

Part of the pun may be that in the United States, the color red is associated with politics of the right, and cou de rouge (without the -p but pronounced the same way coup is) can also be translated as “red neck.” Rednecks tend to vote for right-wing political candidates.