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A friend in Europe asked my advice about a machine carrying this mark, and I don't recognize it. We'd both appreciate any guidance on the subject!

Not familiar to me, but both Thorens and Paillard were based in a place named Sante Croix, and this decal could mean precisely that, Sante Croix...

In a world where companies keep "rebranding" and updating their logo's, its sometimes difficult to determine....

Paillard was similar to this, wheras Thorens commonly used an anchor

I think it's Mermod Frères. Why the letter 'S'? I don't know, but it could have originated with their noted 'Stella' disc musical box.

The website https://www.graphonogram.com/4-documentation.html has lots of old brochures and catalogs from French, German, and Swiss, etc phono makers. A patient scrutiny of that fabulous collection might give the clue.
I don't know who's behind that marvelous website, but although the link provided above goes directly to the Documentation section, it's worthwhile of paying a complete visit. You'll find there many interesting European machines.

Full points to Inigo - exactly correct

Oedipus gave the right name, I only gave a clue to the city...
Mermod not only made machines, but as did Paillard and Thorens, they supplied motors, etc to many phono makers around the world, mostly in Europe...