Fluorinated polymers are attractive due to their special thermal, surface, gas separation, and other properties. In this study, new diblock, multiblock, and random copolymers of cyclooctene with two fluorinated norbornenes, 5-perfluorobutyl-2-norbornene and N-pentafluorophenyl-exo-endo-norbornene-5,6-dicarboximide, are synthesized by ring-opening metathesis copolymerization and macromolecular cross-metathesis in the presence of the first- to third-generation Grubbs’ Ru-catalysts. Their thermal, surface, bulk, and solution characteristics are investigated and compared using differential scanning calorimetry, water contact angle measurements, gas permeation, and light scattering, respectively. It is demonstrated that they are correlated with the chain structure of the copolymers. The properties of multiblock copolymers are generally closer to those of diblock copolymers than of random ones, which can be explained by the presence of long blocks capable of self-organization. In particular, diblock and multiblock fluorine-imide-containing copolymers show a tendency to form micelles in chloroform solutions well below the overlap concentration. The results obtained may be of interest to a wide range of researchers involved in the design of functional copolymers.