We have observed conductance fluctuations (CF) on application of an in-plane magnetic field to 800 nm wide mesoscopic wires fabricated from modulation-doped GaAs/(AlGa)As double quantum well structures. This demonstrates the preservation of electron phase coherence in the presence of inter-well tunnelling and intra-well scattering. The CF disappear when the magnetic field becomes large enough to suppress tunnelling between the quantum wells, and the CF amplitude is lower in samples with thicker tunnel barriers. The wires also display a strong magnetoresistance feature as the quantum wells are decoupled by the in-plane magnetic field. This has been seen previously in macroscopic Hall bars, but is modified due to size effects in the wires.