This happened some way back when I lived in Germany, had a German PPL (pre-JAR), no IR, and was flying a D-Reg PA28
On a VFR flight across France to Germany, I got myself into a bad pickle weatherwise
and decided to land in a field instead of pressing on and entering IMC - no other way out that I could see.
This of course is highly visible - gendarmerie, local press, and their AAIB all were on the scene, but no harm done, and next day we re-launched the aircraft and went on.
The French CAA looked at the incident, wrote a report (in French) to the German CAA (LBA) saying that, with the weather reports that I had, I should have expected the bad weather (which I did) and not taken off or diverted much earlier (which i didn't), so I deserved "at least a severe admonishment" or a penalty in their view.
From that point, it was in the LBA's court.
The German LBA forwarded this letter and a translation to me with the request to comment and a letter effectively being a notice of intention to prosecute. After outlining my sequence of events, which pretty much agreed with the French, as well as agreed with their view that I should have turned around a lot earlier (duh!) and being worded with genuine "I have learned my lesson" attitude, the LBA then closed the case without further prosecution - which in these cases is probably best practice, because prosecuting this sort of thing beyond a "written warning" is stupid as it sends entirely the wrong message to VFR Pilots in marginal weather.
So in my experience, the foreign CAA tells your CAA what happened, and your CAA prosecutes you or not based on their practices and based on the facts, i.e. in theory it should not be that different from a local incident. Don't know what the UK CAA will do with letters in French, though, they might go straight into the bin, or if they care as much about the Paris TMA as they care about London ;-)
Wether the above is true for more serious things like landing unannounced at Charles de Gaulle after flying loopings on their three mile final I don't know, they probably will arrest you on the spot and want to prosecute that directly.