The origin of "welcome" seems to be "will come", not "well come". This is clear from the German version "Willkommen", which is closer to the original proto-germanic "wiljakumo" and is directly related to the rather dated German expression "Will [er/sie] kommen!" ("Let him/her in, or "Will he/she come [in]!"), or even to English "will ya come!". The connection of "will" and "come" signals the desire to receive the guest.

The french "bienvenue" seems to be a too-literal translation from wiljakumo [0]. A similar construction is missing in Latin.

[0] https://en.wiktionary.org/wiki/bienvenue#Etymology