You have two terms here and they will have to be combined with the other bits. I suggest this order.

First, "blanc de soutien" is a white base, also referred to as an underbase or undercoat, when you are printing on a transparent or metal substrate instead of white paper. Normally, four-colour printing, commonly known as CMYK ( https://en.wikipedia.org/wiki/CMYK_color_model ; https://fr.wikipedia.org/wiki/Quadrichromie ), is done on the white ground of the paper, without which it won't look right, so you have to supply a white ground digitally:

Qu’est ce qu’un blanc de soutien ?
https://sprint-for-print.com/faq/quest-ce-quun-blanc-de-sout...

"Color White Print Modes
Intended Use: Most often used for second surface printing (mirrored image on the back of a transparent substrate). [...]
Third Party Preparation (Send with Underbase): Turn on Layer Profiles for the Color-White Queue and turn on White Underbase in the Bitmap Processing options"
http://www.directcolorsystems.com/wp-content/uploads/2015/11...

"En vitro" (short for "en vitrophanie") means printing on the back surface of a transparent substrate such as plexiglass. Of course, you have to print a mirror image so it's the right way round when seen from the front. As the passage I've just quoted indicates, this is known as "second surface printing". You'll also find it called reverse printing in some places, but this term has another meaning and I would avoid it.

"Comme tout support transparent, il peut être imprimé en face avant ou en vitrophanie (lecture miroir) sur la face arrière, ce qui donne un effet de relief au visuel."
https://mobiliersbois.onf.fr/onf-catalogue.pdf

"Les panneaux en Plexiglas (ou plexi diffusant ou pmma diffusant) peuvent être transparents ou diffusants pour caissons lumineux. Ce matériau rigide peut être imprimé, pelliculé, vernis, découpé et personnalisé. Il peut être imprimé recto ou verso en effet miroir (vitrophanie avec un blanc de soutien total ou sélectif)."
https://123panneaux.123imprim.com/imprimer-impression/plexig...

"Second-Surface
Refers to an item made of a clear substrate where the image is reversed and produced on the backside (or second-surface) of the substrate for viewing from the front side. Products that have second-surface printing or engraving have an advantage of having the clear substrate protect the image from abrasion, chemicals, and/or fading."
http://www.cuttingedgeinc.com/ref/gs2.htm

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Note added at 8 hrs (2018-07-12 07:08:58 GMT)
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By the way, a "blanc de soutien" is used for things like tee shirts when printing a coloured design on a dark ground:

"Sur ce type de motif nous avons un blanc de soutien (sous-couche blanche), une couche de gris et une couche de blanc (appelé blanc de réhaut)."
http://teeshirtmania.com/7_tech/serigraphie.html

And it's known there too as an underbase:

"To Underbase or Not to Underbase"
https://www.gooten.com/blog/gooten/2016/02/22/to-underbase-o...

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Note added at 8 hrs (2018-07-12 07:14:11 GMT)
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I've just realised I failed to quote the bit that used "en vitro" from my French source. Here it is, just to dispel any possible doubts:

"Comme tout support transparent, il peut être imprimé en face avant ou en vitro (lecture miroir) sur la face arrière (le visuel est alors protégé par l’épaisseur de la face avant)."
https://123panneaux.123imprim.com/imprimer-impression/plexig...