PtSe2 is an emerging layered two-dimensional material of applied interest. Its monolayer shows promising properties for applications in electronic devices, while the bandgap of a multilayer PtSe2 film can be tuned via changing its thickness. In this work the bilayer PtSe2 thin films are investigated as an example of structural engineering with first-principles calculations. Various van der Waals corrections schemes are firstly discussed, and the optB86b scheme shows a better description of the semiconductor-metal transition for PtSe2 films. Six bilayer PtSe2 thin films in different stacking modes are constructed in order to structurally tune the electronic and transport properties. The bandgap can be effectively broadened with the structural engineering for wider potential applications. The carrier mobility, dynamical stability and Raman spectra are also calculated and discussed.