Regarding what may happen, the worse conceivable outcome is being forced to turn back, especially on your way out. But I assume that even if there is a border check, it would most likely be possible to talk your way out of it.
I am not sure for Switzerland but a fine is not a risk in France, you are supposed to have an official form of ID to cross the border but it's not an offense not to have one within the country. So even if, formally, your attestation is not enough (and it might be for all I know), there is no legal basis to impose a fine or anything. The police could retain you for some time to ascertain your status but with so much evidence of who you are, the fact you are an EU citizen and actually work for a French diplomatic mission, it would just be a waste of time for them (you have a right to be there regardless of any documentary issue and there is no way on earth it would end up in a forcible removal).
Also, my personal experience with this border (which I have had many occasions to cross over the years) is that things are more-or-less back to normal there. A spot check is always possible but when police is present (which it isn't, most of the time), they usually just look at you and wave you through without asking any question. The only place where I have seen systematic document checks is when boarding French trains at Geneva train station.