Quantum Field Theory vs M-theory?

They are not contradictory. QFT is recognized as only an "effective theory", or approximation, at low energy. "Low" is actually quite high - as high as can be achieved today with particle accelerators, but many orders of magnitude lower than needed to test more fundamental theories like M-theory. QFT works great, but has dozens of arbitrary parameters that just have to be measured and igned to constants in the theory. It is also known to be inconsistent with General Relativity (theory of gravity) at very high energy.