Making full use of renewable biomass resources to develop biobased polyester plastics with balanced performance is an important part of achieving a low-carbon circular economy. As a representative variety of biobased furan polyesters, the insufficient mechanical properties limit the application of poly(butylene furanate) (PBF) toward sustainable film materials. This study proposes a trade-off strategy by inserting the rigid biobased 2,3-butanediol (2,3-BDO) unit into the PBF molecular chain. The results show that inserting a small amount of 2,3-BDO can simultaneously realize the strengthening and toughening of PBF. When the content of 2,3-BDO reaches only 4 mol%, the copolymer possesses the tensile strength of 67.0 MPa with the elongation at break of 556.2 %. More appealingly, the crystallizability and barrier properties of copolymers can still be maintained to a certain extent. In general, by inserting a small amount of rigid 2,3-BDO unit, the fully biobased copolyesters can achieve a good balance in terms of crystallization, mechanical, and barrier properties, guaranteeing them to meet the requirements where high strength and toughness are needed.