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Looking at it, it does look like a diminutive of cendre (https://en.wiktionary.org/wiki/cendre#French), which you can compare the name's make-up with Sandrine.
Which leads me to this next point - both Cendrine and Sandrine are pronounced the same and if you look at this chart (https://www.behindthename.com/name/sandrine/top/france?compare=Cendrine&type=percent), you would notice that Cendrine came to be used most often when Sandrine was at its peak.

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