What is this Model and is it Authentic?

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It’s real. Small modification, but nothing that affects the watch.

some models used a curved clamp and the back to hold the movement in place to keep from lifting. Poor design.

someone placed a flat added clamp to hold the movement in place. Only problem is the incorrect type of screw, but can be left as is.

reference number on inside back. The 4 digits

Not all models have names.
 
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Is this a 30.10 SC or a 351 bumper? Scan with the rotor moved would help with that determination.
 
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Nice watch.
The casemaker is Manufacture Favre & Perret SA, based and active in Le Crete-du-Locle since 1934.