Measuring isotopic ratios is a sensitive technique to obtain information on stellar nucleosynthesis and chemical evolution. We present measurements of the carbon and sulphur abundances in the interstellar medium of the central region of our Galaxy. The selected targets are the +50km/s Cloud and several line-of-sight clouds towards Sgr B2(N). Towards the +50km/s Cloud, we observed the J=2-1 rotational transitions of ^12^C^32^S, ^12^C^34^S, ^13^C^32^S, ^12^C^33^S, and ^13^C^34^S, and the J=3-2 transitions of ^12^C^32^S and ^12^C^34^S with the IRAM-30m telescope, as well as the J=6-5 transitions of ^12^C^34^S and ^13^C^32^S with the APEX 12m telescope, all in emission. The J=2-1 rotational transitions of ^12^C^32^S, ^12^C^34^S, ^13^C^32^S, and ^13^C^34^S were observed with ALMA in Sgr B2(N)'s envelope, with those of ^12^C^32^S and ^12^C^34^S also observed in the line-of-sight clouds towards Sgr B2(N), all in absorption. In the +50km/s Cloud, we derive a ^12^C/^13^C isotopic ratio of 22.1^+3.3^_-2.4_, that leads, with the measured ^13^C^32^S/^12^C^34^S line intensity ratio, to a ^32^S/^34^S ratio of 16.3^+3.0^_-2.4_. We have also derived the ^32^S/^34^S isotopic ratio more directly from the two isotopologues ^13^C^32^S and ^13^C^34^S, which leads to an independent ^32^S/^34^S estimation of 16.3^+2.1^_-1.7_ and 17.9+/-5.0 for the +50km/s Cloud and Sgr B2(N), respectively. We also obtain a ^34^S/^33^S ratio of 4.3+/-0.2 in the +50km/s Cloud. Previous studies observed a decreasing trend in the ^32^S/^34^S isotopic ratios when approaching the Galactic centre. Our result indicates a termination of this tendency at least at a galactocentric distance of 130^+60^_-30_pc. This is at variance with findings based on ^12^C/^13^C, ^14^N/^15^N and ^18^O/^17^O isotope ratios, where the above-mentioned trend is observed to continue right to the central molecular zone. This can indicate a drop in the production of massive stars at the Galactic centre, in the same line as recent metallicity gradient ([Fe/H]) studies, and opens the work towards a comparison with Galactic and stellar evolution models.