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) Å, b = 6.03(5) Å, c = 12.3(1) Å, α = 110.1(2)°, β = 121.1(3)°, γ = 100.6(2)°). 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 α- and β-forms.