I'm trying to find how I could translate 'Application Spontanée' from french.
Is there an expression in english to talk about when you apply at an employer, but without any attached open job offer?
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If you apply for a job without being asked in a related offer of such a position, you are filling out an unsolicited application. The employer did not ask (solicit) you to submit it.
Unsolicited = Not looked for or requested; unsought: an unsolicited manuscript; unsolicited opinions.
Note that unsolicited does not mean unwanted:
Nothing is more welcome than an unsolicited complement.
Generally, reaching out to a company or prospective contact that has not solicited that contact is referred to as a cold call or cold contact. This term is often used to describe an attempt to sell a product or service to that company, but broadly speaking, inquiring about a job that may or may not exist is a way of offering your services.
See this blog about job searching, for example: