Impression de photos

CMJN is I think just the French-language transliteration, of what in English language would be CMYK (Cyan Magenta Yellow Black). This format is not sensible for the end user to create, in my opinion. Only the printing company has the specific knowledge of the printing equipment, ink and paper that would be needed to set the various conversion options most appropriately.

The format of image (RGB: red green blue) which Lightroom does output, is usually agreed to be the most suitable to send for printing. That can then use a standard colour model without refererence to any particular printing technology.  

The important matters are bit depth (8 or 16 bits per colour channel); resolution (how many pixels are included in the output file); colourspace - and this will almost always be a standard colourspace such as AdobeRGB or sRGB, except in the unusual case where the printing company has made its own custom ink and paper calibration profiles available, and needs you to convert the image according to these.

In the case of TIFF there are many different saving options, so it is a very good idea to check with the printing company EXACTLY what specification of TIFF they are expecting; or otherwise to make them justify why they cannot accept a (high quality, full resolution, suitable colourspace) JPG.

If the printing company is going to work further on what you are sending, then yes TIFF may be preferable. That leaves them more potential to adjust the image without causing ugly effects.

But you still need to know what bit depth, colourspace, resolution (and also what lossless compression setting) they expect. It is in everyone's interest for them to supply these details to you.