For one, you may not be 'legally' permitted to dump the water into the wetlands. Assuming that you can't, you're left with using the french drain or bypassing that and pumping elsewhere.
Unless I'm missing something, the french drain isn't suppose to fill up w/water. It's purpose is to 'channel' exess water either to a pump or some place else where the water is taken AWAY from the problematic area. So if the french drain is 'connected' to the sump pump via pipes AND the pump pit is filling (and emptying), then I think all is well. Soooo, where does that leave us? It sounds like you need to keep the water moving AWAY from the problematic area (again.)
If you can use your storm sewer, then tap into that. If not, you're left with building some sort of pipe system to get the water away. Be SURE you know how HIGH and how FAR your particular pump's Discharge Line can handle. Also, the DIAMETER of the pipe is important. For example, you may have a pump model that can pump UP 6' with a 'run' of 15' using a 2" line. Understand, that's the MAXIMIM (in this example.) And when you 'operate' your equipment at the EDGE of the limit, your unit will work very hard and have a relatively short life. Keep this in mind whatever you do. Maybe at some 'point' in the piping you can use gravity.
Lastly, they do make battery backup sump pumps (as 1 kit.) You can also buy a battery backup that's separate from the unit. BOTh of these models assume the pump either works, directly with D/C current or has the capability to do so. If the unit is strictly an A/C unit, then you'll need a power generator hooked up to the Breaker Panel in the basement, and so on. (YOu really don't want this.) Your best bet is an AC/DC unit. Basement Watchdog makes one for about $450 at Home Depot. Check it out, or at least what it can do for you.