We can look at the German studies immediately preceeding FCAS (DLR Future Fighter Demonstrator, aka Project Diabolo).
The FFD’s net thrust requirement was 112.7kN dry / 177.1kN wet (per engine). This required a 5m long engine with 1m inlet diameter, weighing 1875kg. Thrust also quoted elsewhere as 124kN dry / 183kN wet… possibly gross (uninstalled) engine rating.
The FFD design is quite big… 20.3m long x 14.8m wide with a 100m2 wing. Empty weight is ~16.5t. Take off weight clean is 28.3t with 8x AAMs (1.8t) and 10t internal fuel, increasing to 29.4t in air to ground configuration with internal weapons (4x AAMs + 4x 1,000lb JDAMs). Max take off weight is ~35t with external load. Combat radius is 780nm hi-hi-hi with internal fuel and 2.5min combat, or 550nm with 1hr CAP loiter.
I find these thrust numbers rather high IMHO. Dry thrust is driven by the Mach 1.4 supercruise requirement and wet thrust by requirements for supersonic maneuverability and Mach 2.0 top speed… see charts below. In addition, the wing is oversized (100m2) in order to enable subsonic cruise at 50,000ft, which increases structural weight and thrust requirements.
So perhaps thrust requirements could be cut by 10-20% to ~100kN dry and ~150kN wet with a few performance compromises (eg. supercruise at Mach 1.2 vs 1.4, top speed Mach 1.8 vs 2.0, subsonic cruise at 45kft vs 50kft). Also I would expect Dassault to be able to optimize the design a fair bit (eg. FFD weapons bay volume seems quite oversized).