"Lunette de bouches" is called "Alignment Sights" by GICAT, which is the professional group representing the industrial sector supplying equipment to the French Land forces and exports Land and Air land equipment. I guess they know what they are talking about. I also think that they have mispelled "Alignement Sights" on their website, should read "Alignment Sights".

Given the following reference to these things being used on mortars, I doubt it's a sighting (i.e. aiming) device, something like the polar alignment scope on the side of a telescope.

LUNETTE DE BOUCHE POUR canon et MORTIER. • Goniomètre d’artillerie pour canon et mortier. ADRESSE. 27, rue Georges COLLIN • 91320 WISSOUS ...
www.gicat.com/fr/adherents/scrome-63.html

Only very high velocity firearms used at short distances will have anything remotely approaching "line of sight" accuracy, i.e. the trajectory of the munitions will be a curve, in the case of a mortar a very distinct parabola; there would therefore be no point at all in sighting/aiming down/up the barrel.

I tend to think it might therefore be an optical instrument for checking the geometry of a barrel and/or adjusting the aiming sights (though in the case of a mortar, I still fail to see the point):

On MET DANS LE CANON qui est le reference UNE LUNETTE DE BOUCHE une SORTE DE LONGUE VUE reglée en usine qui quand on regarde par un optique latéral, renvoie une image inversée de la forme géométrique,lorsque les deux images sont correctement superposées l'ame du canon est calée sur la mire.
Là et seulement là on regle les lunette tireur et chef et la MG de bord.Là c'est plus simple car on vise plein centre avec la croix de simbleautage ou un autre repere qui est prévu à cet effet dans le réticule de la lunette
http://dday-overlord.forumactif.com/chars-engins-blindes-et-...

Barrel Borescoping
Borescoping is the alignment of the barrel with the screw. Their clearance can range from 0.05 to 0.20 mm (for small- to large-diameter screws) on all sides of the screw. Borescoping alone is not a guarantee of perfect performance.
With an ALIGNMENT SCOPE one can TELL WHAT THE INTERNAL SHAPE OF A BARREL IS AT ANY POINT— whether it is a straight, curved, or even S-shaped as a result of machining or subsequent wear (see the Screw Wear Guide in Chap. 11).
http://www.mechanicalengineer.cc/mechanical-engineering-cate...
(this appears to concern not gun barrels but the barrels of injection moulding machines)

Taylor-Hobson optical ALIGNMENT SCOPE and a TARGET SLED PULLED THROUGH THE GUN. The measurements have also been done by an outside group from Aberdeen Labs. ...
ieeexplore.ieee.org/iel1/20/5024/00195609.pdf?arnumber=195609

51-1000 ALIGNMENT TELESCOPE
Specifications
An economical and accurate OPTICAL ALIGNMENT INSTRUMENT well-suited to applications not requiring a micrometer. Magnification 34x at infinity. All W-K alignment telescopes are made of heavy walled, heat treated, alloy steel tubing meeting AIA specifications. Illumination is available by low voltage transformer and bulb.
http://www.warrenknight.com/warrenknight.php?ANYSEARCH=magni...

These seem to be used to check that the sights are aligned with the bore of the gun/mortar.
You can see a picture at the ordnancemarine link.

Since I posted my boresights answer, I found this, which may be slightly better.
This Pdf document gives photos and description of operation:

www.meditec.zeiss.co.jp/C1257088004A3F3C/EmbedTitelIntern/5...$File/53_0840e_CalibrationAndAllignment.pdf