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We report an astrochemical study on the evolution of interstellar molecular clouds and consequent star formation in the center of the barred spiral galaxy M83. We used the Atacama Large Millimeter/submillimeter Array (ALMA) to image molecular species indicative of shocks (SiO and CH₃OH), dense cores (N₂H⁺), and photodissociation regions (CN and CCH), as well as a radio recombination line (H41α) tracing active star-forming regions. M83 has a circumnuclear gas ring that is joined at two intersections by gas streams from the leading-edge gas lanes on the bar. We found elevated abundances of the shock and dense-core tracers in one of the orbit-intersecting areas, and found peaks of CN and H41α downstream. In the other orbit-intersection area, we found a similar enhancement of the shock tracers, but less variation of other tracers, and no sign of active star formation in the stream. We propose that the observed chemical variation or lack of it is due to the presence or absence of collision-induced evolution of molecular clouds and induced star formation. This work presents the clearest case of the chemical evolution in the circumnuclear rings of barred galaxies thanks to the ALMA resolution and sensitivity.