The Lagrangian theory developed for fountains in a stationary fluid is extended to predict the path and breadth of a fountain in a one- and two-layer fluid with a moderate crossflow. The predictions compare well with the results of laboratory experiments of fountains in a one-layer fluid. The empirical spreading parameter determined from the one-layer experiments is used in the theory for fountains in a two-layer crossflow. Though qualitatively correct, the theory underpredicts the height and radius of the fountains. Similar to the behaviour of fountains in two-layer stationary ambients, the fountain in a two-layer crossflow is observed to exhibit three regimes of flow: it may penetrate the interface, eventually returning to the level of the source where it spreads as a propagating gravity current; upon descent, it may be trapped at the interface where it spreads as a propagating intrusion; it may do both, partially descending to the source and partially being trapped at the interface. These regimes are classified theoretically and empirically. The theoretical classification compared the buoyancy excess of the descending flow to the density difference between the two layers. The regimes are also classified using empirically determined regime parameters which govern the relative initial momentum of the fountain and the relative density difference of the fountain and the ambient fluid.