This paper describes the synthesis, crystal structure, and physicomechanical properties of a biobased polyester prepared from 2,5-furandicarboxylic acid (FDCA) and 1,4-butanediol. Melt-polycondensation experiments were conducted by a two-stage polymerization using titanium tetraisopropoxide (Ti[OiPr](4)) as a catalyst. Polymerization conditions (catalyst concentration, reaction time and second stage reaction temperature) were varied to optimize poly(butylene-FDCA), PBF, and molecular weight. A series of PBFs with different M-w were characterized by DSC, TGA, DMTA, X-ray diffraction and tensile testing. Influence of molecular weight and melting/crystallization enthalpy on PBF material tensile properties was explored. Cold-drawing tensile tests at room temperature for PBF with M-w 16K to 27K showed a brittle-to-ductile transition. When M-w reaches 38K, the Young modulus of PBF remains above 900 MPa, and the elongation at break increases to above 1000%. The mechanical properties, thermal properties and crystal structures of PBF were similar to petroleum derived poly(butylenes-terephthalate), PBT. Fiber diagrams of uniaxially stretched PBF films were collected, indexed, and the unit cell was determined as triclinic (a = 4.78(3) angstrom, b = 6.03(5) angstrom, c = 12.3(1) angstrom, alpha = 110.1 (2)degrees, beta = 121.1(3)degrees, gamma = 100.6(2)degrees). A crystal structure was derived from this data and final atomic coordinates are reported. We concluded that there is a close similarity of the PBF structure to PBT alpha- and beta-forms.