English borrowed this word twice, and the first try did not take.
Etymonline says it appeared as Middle English entreprenour in the late 15th century and then dropped out of use. English reborrowed it from French in 1828, with a very specific meaning: the manager or promoter of a theatrical production. The sense of a "business manager" followed in 1852.
The French is an agent noun from entreprendre, "to undertake." That verb is entre-, "between," plus prendre, "to take," which contracts Latin prehendere, "to seize." The related noun enterprise is the same verb in its past-participle form, and it entered English in the early 15th century meaning "an undertaking."
In France the word long had a darker flavor. A Mises Institute article says it first suggested someone active or risky, sometimes in violent undertakings. By the 16th and 17th centuries it meant a government or military contractor, such as a man who built public works or supplied an army. The author calls this figure a "political entrepreneur." He describes Bélidor's engineering handbook of 1729 as the last word on this type, portraying the contractor as devious and undependable.
Richard Cantillon changed the meaning. His Essai sur la nature du commerce en général is said to have introduced the new idea around 1730. The manuscript was apparently finished before his death in 1734, but was not published until 1755. In it the entrepreneur is someone who buys at a known price and sells at an uncertain one, taking the risk in between. That moved the word from the public sector to the private market.
Cantillon's idea spread through manuscript circles before publication. Jean-Baptiste Say later took a more elaborate view of the entrepreneur, but the same article says Cantillon's narrower definition was already common usage by his day and was used without attribution.
Notice what the English history adds. The word came into English as a theater manager, not a founder, and the risk-bearing business sense settled in only later.