We use resonant inelastic x-ray scattering to investigate charge-stripe correlations in La1.675Eu0.2Sr0.125CuO4. By differentiating elastic from inelastic scattering, it is demonstrated that charge-stripe correlations precede both the structural lowerature tetragonal phase and the transport-defined pseudogap onset. The scattering peak amplitude from charge stripes decays approximately as T-2 towards our detection limit. The in-plane integrated intensity, however, remains roughly temperature independent. Therefore, although the incommensurability shows a remarkably large increase at high temperature, our results are interpreted via a single scattering constituent. In fact, direct comparison to other stripe-ordered compounds (La1.875Ba0.125CuO4, La1.475Nd0.4Sr0.125CuO4, and La1.875Sr0.125CuO4) suggests a roughly constant integrated scattering intensity across all these compounds. Our results therefore provide a unifying picture for the charge-stripe ordering in La-based cuprates. As charge correlations in La1.675Eu0.2Sr0.125CuO4 extend beyond the lowerature tetragonal and pseudogap phase, their emergence heralds a spontaneous symmetry breaking in this compound.