The physical properties of Mn3CuN were studied using thin films. We found that an annealing process was very effective to improve the film quality, the key of which was the use of Ti that prevented the formation of oxide impurities. Using these high-quality thin films, we found strong strain dependence for the ferromagnetic transition temperature (T-C) and a sign change of the Hall coefficient at T-C. The analysis of Hall coefficient data revealed a sizable decrease of hole concentration and a large increase of electron mobility below T-C, which is discussed in relation to the electronic structure of this material.