I personally wouldn't use words like "impossible" because there's always a chance of something happening, but back to your point.
A refugee is someone who is seeking refuge from something, yes? In this case, a Syrian refugee is someone is trying to flee from war. This person very likely had a job in Syria before things went to pot, possibly a family, friends, etc. In short, a life they generally enjoyed. The war in question includes ISIS as one of the active forces involved.
So, does it make sense that someone who is fleeing from war would seek to create a war-like situation in the country they're fleeing to, to aid one of the belligerents in the war they're fleeing from?
Here's a much more plausible explanation: Someone got in to France pretending to be a refugee.
One could argue that such a person genuinely sought refuge in France then was radicalised, but again I think it's a heck of a lot more likely that such a person would have joined in the war in Syria in the first place, for the reason I already stated.