What is the correct job name: Marketing Product Manager or Product Marketing Manager?

We'd normally call the job Product Marketing Manager, although companies are welcome to invent any titles they want.   I live in a valley where some people insist on being called "Chief Growth Hacker." I could imagine a company using the other title for the marketing portion of its product line... for instance if they develop online marketing/sales tools, they might assign product management responsibility for part of the product set, and have a "Marketing Product Manager" in charge of the Marketing stuff and a  "Sales Product Manager" handling the Sales features and a  "Professional Services Product Manager" worrying about features for bidding/staffing one-time consulting services.

Certianly what we see most often os product marketing manager. As Geraldo said, it's a manager of the marketing of a product. That is, the go-to-market activities. It's challenging to map titles to activities because there are so many titles to consider. I think it helps to change "manager" to "expert" and see if the title still makes sense. There are four types of expertise we see deployed in product management. I touch on each in my free ebook, Product Management Expertise at http://www.under10consulting.com/writing/expert

The correct use is Product Marketing Manager.   Marketing Product Manager would imply it is a product management role in a marketing department or a manager of a 'marketing product'   Product Marketing Manager means it is someone who manages the marketing of a product, which is an accurate description of the role.

For your "Chef de Produit" role, I think the correct translation is simply "Product Manager." Depending on the organization, "Product Manager" could be a member of Marketing, Engineering, Products or even Sales. So I agree that the group a position belongs to (e.g. "Marketing") need not be reflected in the job title. For the "Product Marketing Manager" title that you see in the U.S., that refers to a more outbound (external facing) role, which tends to be different from Product Manager, which is inbound (internal facing). For the "Product Marketing Manager" title, the "Marketing" refers not to the team the person belongs to, but the function (e.g. marketing products or taking products to market). Hope that helps.

Product Marketing Manager. The core function of the role is marketing, specifically creating awareness, differentiation and demand - in this case - of the product. 'Product' is an adjective describing the type of marketing (as opposed to Corporate Marketing which aims to relate company value, Product Marketing relates product value).

My impressionis that "Produit Marketing" is a kind of verbal chimera -- on l'appelerait en englais un http://en.wikipedia.org/wiki/Portmanteau . Marketing is not exactly a proper French word... So I would say you should look at definitions of inbound and outbound product management in English, and see which responsibilities this job includes, then choose Product Manager if it's inbound, Product Marketing if it's outbound, or if both are included, just make it explicit-- "Product and Product Marketing Manager" or "VP of Product and Product Marketing" or something like that..