I think if FR/MO'L were to go out and target EI, shareholders in FR could justifiably ask why they are not targeting other flag carriers, which have considerably lower margins and struggling much more.
There is also a potential advantage EI has on longer flights - not just the better service, but the fact that FR (so far) prefers not flying overnight. If EI were to serve the likes of ATH, IST, LCA, etc, it could operate the service overnight from Dublin and have it back to DUB in time for another day's flying; if FR were to do so, it would do the route by daylight, eating up utilisation which could be used on shorter routes (preferably elsewhere).
I agree with your comment that there is a market for both airlines to exploit without crossing each other's paths and that FR is not necessarily the winner if they do, but I still think FR is going to make life as tough as possible in the lead up to EI's privatisation and don't think that won't include spreading scare stories or planting rumours like long haul routes or the like - purely to spook investors.