This introductory essay presents the debate focused on the Abbé Jean Paulmier's Mémoires touchant l'establissement d'une mission chrestienne dans le troisième Monde, Autrement appellé, La Terre Australe, Meridionale, Antartique, & Inconnuë, published in 1664. The Abbé claims to be descended from a native of the Terres Australes, Essoméricq, brought to France by the explorer Gonneville in 1505. Based on this contention, the Abbé argues that the French should return to the country discovered by Gonneville and evangelise it. Recent scholarship has come increasingly to question the authenticity of Gonneville and his voyage, as well as Paulmier's genealogy. This article sets out the details of the debate and adds new elements to it, paving the way for the articles which follow, both on the Gonneville controversy and on the beginning of French missionary activity in the Pacific Ocean.