Hi and welcome to Simviation

I have had this problem before.
What has always worked for me is to put more fuel in the plane in the Aircraft Selection page (where you pick the plane to fly). My default flight has 30% fuel set and for whatever reason on some planes that will cause the engine to die shortly after the flight loads. Increasing the fuel to 70% works most times, but I believe on a couple I had to put in 100% before it would keep running.
I don't have the plane you are trying, but I would guess it has a few fuel tanks. Just try putting fuel in all of them to at least 70% (or 100% if you want). Check your takeoff weight though to make sure it doesn't say you are overweight. If it does, boot some passengers. Just pretend TSA said they had to get off the plane, lol.
If there is another fix for this, I don't know of it and hopefully someone that does know will post the solution.
Anyway, I hope adding fuel will get it working for you

EDIT:
I think I found the plane you have and there is a Engine Start Fix for it.
If this is the plane (the top one on this page), get the fix and try it.
http://simviation.com/1/search?submit=1 ... &filename=Also, if you go to Page 1 there is some updated ones that may work better

Actually this one on Page 1 looks like the most up to date version, I think.
FSX PM2 Concorde Redux Package
You might be better off removing the one you now have and installing this one. Sound like it is complete and ready to use.