The present paper investigates the tax returns of French cohabiting couples with children, defined here as neither married nor in a civil union. These couples represent an interesting case, because they form two separate tax units according to French tax laws and must optimally assign their children to one of the parents' tax units to optimize tax rebates. Using administrative tax data and a microsimulation model, we analyze whether cohabiting couples allocate their children to minimize the joint tax burden of the family. We find, however, that children are not optimally allocated in 25% of cases. We interpret the reasons why couples fail to financially optimize their situation by discussing the usual explanations (e.g., transaction costs, "simple rule," inertia) as well as a more specific reason: the potential non-cooperative behavior of cohabiting couples, possibly related to the lack of a binding agreement or potential asymmetries of information between partners. We also find suggestive evidence regarding heuristics (such as the equal split rule for an even number of children), a large degree of inertia (based on fiscal status changes over two years), and possible non-cooperation (suboptimal couples tend to separate more and marry less in the subsequent period).