classic motorcycle forum

Sorry old chap, this bike is a lash up, that engine is out of a lawnmower or some other industrial application.
If you look at the engine plates you will see there is an extra hole sticking out of the front, a sure sign that engine is not out that frame.
I have seen this  kind of set up before.
The carb position is all wrong, and I'm unhappy about the gearbox and the way it is fitted.

Did I ask if it was ever registered in Ireland?

On the head-stock, and as is common to most bikes on the continong, you  should have a small plate on which are stamped various details about the bike,  model, engine size, date of manufacture and so on. Is there one?

It may even have started life as a Kohler-Escoffier, sister to Monet Goyon, like AJS/Matchless.

Time to make a hard decision I think, but FFS, do not spend any money on it,cut your losses.

plate will look similar to this  https://www.ebay.fr/itm/Plaque-de-cadre-moto-Peugeot-/173502648382?nordt=true&orig_cvip=true&rt=nc&_trksid=p2047675.m43663.l44720

or  http://guigui-monetgoyons6vu.blogspot.com/2014/02/plaque-de-cadre.html

and here is a site covering Monet Goyon two strokes for you to look over.

http://www.monet-goyon.net/2tempsAVG.html

I might be wrong about that extra hole, seems to be one on these, so far type ZA2 1931 look close to what yours is meant to be.