In February 1849, Frederic Bastiat wrote an essay Capital et Rente (available in English as Capital and Interest). It had quite some success in the working class and caused some turmoil within socialist ranks. F. Chevé, writer in the socialist magazine La Voix du Peuple (the Voice of the People), wrote an open letter to Bastiat in his magazine to question his essay. Bastiat replied, and Chevé decided to publish the reply, with a counter-reply by Proudhon. The debate went on between Bastiat and Proudhon, until on his 6th and last letter, Proudhon declared the debate closed and Bastiat dead. Bastiat wrote a last reply, but it was not published by La Voix du Peuple (presumably because Proudhon didn't want to continue, and they didn't dare finish the debate on a letter by Bastiat); instead, they published the 13th first letters of the debate as a book Intérêt et Principal. Bastiat published the 14 letters as Gratuité du Crédit, a 242-page book, included in volume 5 of his complete works.
Bizarrely, there is no trace of this on this page on Proudhon, but some of Proudhon's letters (translated to english, including neither the last one, nor any of the replies by Bastiat) can be found in the Anarchist Archives. Letters by Bastiat can hardly be found anywhere. The second letter of the debate is on Bastiat.org (in French). Another related essay by Bastiat, which contains arguments to reply to the last among letters by Proudhon published above, is Maudit Argent (available in English as What is Money?).
At the Bastiat'2001 conference, Alain Laurent spoke about Bastiat's influence on Proudhon and how Bastiat's ideas would slowly percolate in latter works by Proudhon. Unhappily, Bastiat died in 1850, so this influence wasn't as great as it could have been.
