I noticed a similarity between the word Salut in French and the word سلام in Arabic which is pronounced Salaam and they both mean "safety and well-being" and are both used as a general greeting to mean "hello". But Salut comes from Latin which I don't think is related to Arabic in any way. How can that be possible then?
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Like you said, the French term salut comes from Latin and to be precise from salūs salūtis. This term appears in other Romance Languages as well: It. saluto, Es. saludo.
The meaning which is health, well-being, is carried out also by other descendants: It. salute, Es. salud, Port. saúde.
I don't think there is a connection to salaam which actually means peace in Arabic (I think you can confirm this meaning) and is related to the term shalom in Hebrew. You can find more about this on the Wikipedia page for Shin-Lamedh-Mem, the "the triconsonantal root of many Semitic words", at the section Salam "Peace".
According to the same page, this "root itself translates as whole, safe, intact", but the triconsonantal part refers to the Š-L-M, while in salut we miss the last one and we have a T instead.
There seems to be a real closeness in terms of meanings which could be a coincidence. Still, this is just a superficial analysis and I don't have all the tools/resources to absolutely exclude a link.
These words may be related.
The Latin word comes from Proto-Indo-European solu̯os "healthy, whole". It is hypotized to derive from Proto-Eurasiatic calom "to suffice, be full" which also gave reflexes in other Eurasiatic languages such as Eskimo-Aleut ciɫǝ-m, Altaic čā́lo, Uralic cilä, Dravidian sāl-
The Arabic salaam and Hebrew šalom both derive from Proto-Semitic šǝlǝm "healthy, whole", which in turn derives from Proto-Afro-Asiatic s/cǝlǝm "healthy, whole".
Since both Eurasiatic and Afro-Asiatic belong to Nostratic (and considered quite close to each other), it is reasonable to suppose they are related.
Notice also Proto-Sino-Caucasian ʒó̆ɫǝ "healthy, whole" (example from Lak language: cullu-s:a "whole, healthy, undamaged") with Proto-Sino-Caucasian groupped as sister family to Nostratic into Borean.
To add to the previous posts, "Salve" was a common greeting phrase in Sweden during the medieval time, and also has a similar meaning (peace, well-being).