Weak epitaxy growth (WEG) is an effective method in the preparation of high-mobility thin films of disk-like organic semiconductors. The growth behavior and quality of the epitaxial thin film are closely related to the inducing layers. Here, a series of fluorinated molecules, 5,5 ''-bis(3'-fluoro-biphenyl-4-yl)-2,2':5',2 ''-terthiophene (m-F2BP3T), 5,5 ''-bis(3',5':difluoro-biphenyl-4-yl)-2,2':5',2 ''-terthiophene (F4BP3T), and 5,S ''-bis(4'-fluoro-biphenyl-4-yl)-2,2':5',2 ''-terthiophene (p-F2BP3T) as well as a referenced molecule 5,S ''-bis(biphenyl-4-yl)2,2':5',2 ''-terthiophene.(BP3T), are introduced to serve as inducing layers for the epitaxy growth of phthalocyanine. Compared to the non-fluorinated inducing layer, the interactions between the fluorinated inducing layer and phthalocyanine might be relatively strong due to the potential existence of weak hydrogen bonds. The growth behavior and mechanism of phthalocyanine on the fluorinated inducing layers are investigated by atomic force microscopy (AFM), grazing incidence X-ray diffraction (GLXD), selected area electron diffraction (SAED). According to the AFM and SAED, H2Pc presents a selective epitaxy growth depending on the position of fluorine: epitaxy growth on m-F2BP3T and F4BP4T, and nonepitaxy growth on p-F2BP3T. Comparison of CuPc with F16CuPc on monolayer p-F2BP3T further revealed that the uncommon nonepitaxy growth behavior of H2Pc (CuPc) on p-F2BP3T mainly originates from the enhanced interactions between the two types of molecules. As a consequence, the capability of molecules orienting themselves along the surface channel is decreased; meanwhile, the demand of the upper limit of the lattice mismatch is more rigorous for commensurate epitaxy. Finally, the oriented nucleation of H2Pc (CuPc) on monolayer p-F2BP3T is affected, and netlike crystals are formed. The sudden change of H2Pc (CuPc) from multiorientation on monolayer to just one orientation on double-layer p-F2BP3T suggests that there is a critical lattice mismatch value for commensurate epitaxy in WEG when the molecule substrate interactions are enhanced.