Unless there is a reason that you have to return to Dublin, I'm with the others. Fly open jaw: home-Dublin and then Paris-home.
Budget airlines from Dublin to London: BMI and Aer Lingus to Heathrow; and Ryanair to Gatwick, Luton, and Stansted. See www.londontoolkit.com for your transportation options from the airports to central London. Heathrow-London on the tube would be cheapest.
London-Paris: Eurostar is the fastest and most comfortable way. City center to city center in less than three hours. Depending upon seat availability, a return (roundtrip) ticket can be less than a single (one-way) ticket. Just throw away the return portion. Book at www.eurostar.com.
Flying options: Heathrow to CDG on either BMI or British Airways; Luton to CDG on easyJet.
Paris-Dublin: Aer Lingus from CDG; Ryanair from Beauvais.