In France, a proposal was made to substitute a unique labor contract with a degree of employment protection increasing with tenure to the existing open-end and fixed-term contracts. Using survey data, this paper analyzes the social support for this contrat de travail unique (CTU). Contrary to the prediction of insider/outsider theories, support for the CTU comes from insider groups, whereas most outsider groups oppose it. This result may be the consequence of the job protection increasing with tenure. This mechanism could reinforce certain types of market segmentation instead of abolishing employment precariousness.