  The charge density wave in the high-temperature superconductor
YBa$_2$Cu$_3$O$_{7-x}$ (YBCO) is now known to have two different ordering
tendencies differentiated by their $c$-axis correlations. These correspond to
ferro- (F-CDW) and antiferro- (AF-CDW) couplings between CDW in neighbouring
CuO$_2$ bilayers. This discovery has prompted a number of fundamental
questions. For example, how does superconductivity adjust to two competing
orders and are either of these orders responsible for the electronic
reconstruction? Here we use high-energy x-ray diffraction to study
YBa$_2$Cu$_3$O$_{6.67}$ as a function of magnetic field and temperature. We
show that regions of the sample with F-CDW correlations suppress
superconductivity more strongly than those with AF-CDW correlations. This
implies that an inhomogeneous superconducting state exists, in which some
regions show a weak or fragile form of superconductivity. By comparison of
F-CDW and AF-CDW correlation lengths, it is furthermore concluded that F-CDW
ordering is sufficiently long-range to modify the electronic structure. Our
study thus suggests that F-CDW correlations have an important impact on
superconducting and normal state properties of underdoped YBCO.
