Little Greene French Grey is a lovely soft green-grey, but you're paying a premium for the name and the depth of their pigment loading. The good news is there are genuinely close matches for less.
Dulux Valley Rock is the pick of the bunch at ΔE 1.6 from the original (LRV 54). Anything under 2.5 is what we'd call very close, and 1.6 means most people couldn't tell them apart side by side, let alone across a room. It's widely stocked, easy to get colour-matched, and a fair bit cheaper per tin.
If you want something in trade-friendly Crown, Gentle Hush comes in at ΔE 1.8 (LRV 57.9). It reads very slightly lighter and airier because of that higher LRV, which can actually be a bonus in a north-facing room where French Grey can go a touch flat.
For a modern, low-VOC option that's still keenly priced, COAT And Breathe is ΔE 2.4 (LRV 55.8). It's the furthest of the three but still firmly in "very close" territory, and COAT's matt is a genuinely good finish.
The one caveat: French Grey's charm is how it shifts between grey and green depending on light. The cheaper matches replicate the colour faithfully, but Little Greene's higher pigment density gives a slightly richer, chalkier hand on the wall. In daylight you won't notice; in a dim hallway under warm bulbs, the original has marginally more presence.
My advice — buy a tester pot of Valley Rock, paint a decent A4 patch (two coats), and live with it for a couple of days in your actual light before you commit. If it sings, you've saved a fair bit of money for no real loss. If you fall for the depth of the original, then you'll know it's worth the extra.