The nearest train station to Saint-Étienne-De-Fontbellon is Montélimar, which lies on a north-south line served by Lyon airport at one end, with Avignon and Marseille aiports at the other.
Avignon is unlikely to be of much use to you as the flights there from the British Isles are only seasonal and you'd have to get to London City (to access CityJet's service) or Birmingham or Southampton (to use FlyBe's flights) first.
As your post recognises, you can fly from Dublin to Lyon with Aer Lingus. (There is no other operator on that route and there is no service to Lyon from either of Belfast's airports).
Ryanair operates seasonally from Dublin to Marseille but when those flights aren't operating it might be worth considering using Ryanair to travel via Stansted, since Dublin-Stansted and Stansted-Marseille are both operated all year round).
Aer Lingus also operates seasonally from Dublin to Marseille. (There are no flights ex Belfast).
Fares are likely to vary enormously depending upon when you want to travel. For example, return travel from Dublin to Lyon next week would cost you €372. Travelling in October would cost you €129.
Flying to Marseille next week would cost you €280 (return) with Aer Lingus. Their flights only operate until mid-September, but return fares are around €139 towards the end of the booking period. (Note that Aer Lingus only flies that route on Tuesdays, Thursdays and Saturdays).
Ryanair fly to Marseille on Mondays, Wednesdays and Fridays, thus filling in the gaps left by Aer Lingus. Return travel next week would cost you €258. However there are no direct flights after the end of this month.
The rail fare from Lyon-Saint Exupery Airport to Montélimar is typically £58 return for travel in the near future but £33 when booked well in advance. The fare from Marseille Vitrolles Airport appears to be £48 at all times.
http://uk.voyages-sncf.com
Without further information about exactly
when you want to travel, that's probably about as far as I can get but simply post again (with additional information if you need more help).