Abstract Nominalization in French can be done by means of conversion, which is characterized by the identity between the base and the derived lexeme. Since both noun→verb and verb→noun conversions exist, this property raises directionality issues, and sometimes leads to contradictory analyses of the same examples. The paper presents two approaches of conversion: derivational and non-derivational ones. Then it discusses various criteria used in derivational approaches to determine the direction of conversion: diachronic ones, such as dates of first attestation or etymology; and synchronic ones, such as semantic relations, noun gender or verb inflection. All criteria are evaluated on a corpus of 3,241 French noun~verb pairs. It is shown that none of them enables to identify the direction of conversion in French. Finally, the consequences for the theory of morphology are discussed.