Hi from Paris,
After 1933 from Germany and 1938 from Austria, a lot of Jews but also of nazi's opponents could arrive in France.
When WWII started on 1939 September 1st, they had to register and were sent to interment camps as citizens of an enemy country.
Jews could be released if they agreed to enroll French Army in Foreign Legion regiments : men of my family were Austrian Galizianers and did it.
Mostly after the large French round-ups of Jews during July and August 1942, a lot of Jews found a refuge by being smuggled through the Swiss border.
"Being smuggled" because exactly in August 1942, Swiss government decided that being a Jew trying to save his life was not enough a reason to enter legally Swiss.
In Geneva state by itself, nevertheless ca 9.000 did it.
In this area of Geneva lake, relief isn't mountainous but only fields in a valley : I attach some pictures of the place where my mother (13's) crossed the border, as did ca. 200 Bundists of France (families or children alone).
Today, just a border stone in middle of a field...
But, but, but, in middle of this field, you had to cross two barbed wire lines and French / German patrols which shoot on sight.
And when refugees were caught by Swiss border police, they could be returned immediately to French side, sometimes voluntarily in front of these patrols... 

Concerning refugees crossing to Geneva state, state archives still detain a file for each person (even small children, I have copied 200 of them) as do Bern Federal archives.
Most of other Swiss states (cantons) have destroyed these files after WWII...
A lot of books and thesis (the last from Ruth Fivaz) analyze what has been Swiss policy concerning Jewish refugees during WWII.
You have also a Swiss documentary "Memories of the border".
Khavershaft
Bernard Flam
Archives & history of Medem Center - Arbeter Ring of France (Bund / Worker Circle)