Men (and some women, nowadays) usually wear a skullcap known as a kippah or yarmulke, which can be of varying size and any colour - they can even have the names of sports teams or rock bands. A yarmulke provides separation between the Divine and the everyday world, showing respect and reverance toward G-d in doing so. The Talmud tells us that when asked why he always covered his head, Rabbi Honah ben Joshua said "Because the Divine Presence is always over my head" (Kiddushin 31a) and states "Cover your head in order that the fear of Heaven may be upon you" (Shabbat 156b). Observant Jewish men will also commonly wear a hat; often a homberg, fedora or fur striemel as commonly worn by rabbis.
Observant Jewish women, once married, will also cover their heads in public due to the Jewish idea that a woman's hair is one of the chief physical attributes in making her attractive to men. So that she does not attract men other than her husband, she keeps her hair covered. Some very religious women shave their heads and wear a wig, which will then also be covered by either a hat or a headscarf; but this is increasingly rare in the modern world except among the Charedim (highly religious and orthodox Jews) and some elderly women.
Men (a boy over the age of 13) Wear a kippah/ skull cap
People who observe the Jewish religion dress modestly. In addition, men and married women cover their heads; and men wear tzitzit (Numbers 15:37-41).
A Jewish batch.
Kippa
Well i would expect most French people to wear or have hair on their head.
No, there is really no relation of the two head covers. In the early day of the Church, church buildings had no heating. Most of the clergy had the top of their heads shaved (tonsure) and would wear the zucchetto to keep their heads warm.
perhaps civil war soldiers of Jewish descent.
Men wear suits and ties, and women wear dresses or slacks.
Because it keeps their heads warm!!
to protect their heads from injury.
Forehead protectors or headbands
Why would you want to? No law against it, but people would mistake you for Jewish.
In addition to the regular clothing that other men wear, Orthodox Jewish men generally wear a kipa ("yarmulke" in Yiddish; a small, round skullcap) on their heads and four-cornered fringed garments colloquially referred to as tzitzit (the word "tzitzit" in Hebrew actually refers to the fringes) under (or over, depending on personal preference) their shirts.