There are plenty of examples on internet with this expression.

in modern French, we'd say deS coups de plumE (no S)

As I read it, the French means that the involved parties cannot settle the score between them merely by exchanging opposing views in writing; instead, something stronger than that kind of polemic is required. Here are some examples of the expression "duel of pens" used to express a similar meaning:

From http://derrickjeter.com/2011/02/18/founding-fathers-friday-c... :
"Upon his return to his estates in Maryland, he found his colony ill at ease, bristling under the recent passages of the Stamp Act. Within a few years, Carroll would anonymously take the patriot’s part in a duel of pens, played out in Maryland papers."

From a book review at https://www.goodreads.com/book/show/106238.Miss_Manners_Guid... :
"Judith Martin's writing is bitingly funny and entertaining as all get-out. In another age, she would have held her own in a duel of pens with Dorothy Parker or Oscar Wilde."

From http://www.sarasolo.com/mn2.html :
"Since 1975, when the publisher, Knopf, hoping for a cover blurb, sent him an unbound manuscript of The Woman Warrior, Chin has been hammering away at Kingston in essays, academic conferences and newspaper articles. Their duel of pens has enlivened university conferences and inspired academic papers, doctoral dissertations and college lectures."

From http://text.egwwritings.org/publication.php?pubtype=Book&boo... :
"Polemics being the order of the day, he engaged in many a duel of pens, one in particular being a sharp exchange with the Spiritualists. Sometimes his rebuttals were devastating."

From http://trove.nla.gov.au/ndp/del/article/59056828 :
"The fact that Mr. Elkan now professes to admire the brave British commander of the Titanic and to admit that every man worthy, the name will do his best to succour the women and children (he doesn't say 'first'), proves that I have not fruitlessly taken him to task for his initial letter. I have so often publicly chastized him with the pen that in the duel of pens that he would have, I may already be adjudged the victor..."

From a New York Times article from 1914 at http://query.nytimes.com/gst/abstract.html?res=9502E7DF1638E... :
"THE battle of the armies is over and the battle of the books has begun. Viscount French has fired the first gun in a duel of pens that will surely eclipse the similar duels that raged - and still rage, for that matter..."


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Note added at 18 hrs (2015-01-16 09:39:32 GMT)
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@Daryo:

It seems to me that the speaker does not want to engage in the sort of written response that would lead to nothing more than a "duel of pens" precisely because that kind polite, polemical form of attack on his part would be inadequate. It would not even the score. He thinks something stronger is required, an approach so powerful that not even derision could defeat it.
In other words, I'm suggesting that "duel of pens" is to be read in a deprecatory way. The speaker is rejecting that approach; he does not intend to use his pen to that end.
While don't think that this is the only possible translation, I do think it is an option that makes sense and transmits the meaning of the French text.