The zirconium content of the alloy composition of a copper alloy wire is 3.0 to 7.0 atomic percent; and the copper alloy wire includes copper matrix phases and composite phases composed of copper-zirconium compound phases and copper phases. The copper matrix phases and the composite phases form a matrix phase-composite phase fibrous structure and are arranged alternately parallel to an axial direction as viewed in a cross-section parallel to the axial direction and including a central axis. The copper-zirconium compound phases and the copper phases in the composite phases also form a composite phase inner fibrous structure and are arranged alternately parallel to the axial direction at a phase pitch of 50 nm or less as viewed in the above cross-section. This double fibrous structure presumably makes the copper alloy wire densely fibrous to provide a strengthening mechanism similar to the rule of mixture for fiber-reinforced composite materials.