I am a fan of The Great War by Warhammer Historicals, which is sadly out of print. It is a fast and easy game that operates on a stripped-down version of the Warhammer 40,000 3rd edition rules. My only quibble would be the lethality is a little high, but it is hard to say that is wrong.
I used to play The Great War Rules a lot and agree the lethality was high which I thought was due to I Go You Go system which tended to mean the attacker advanced only to be mowed down by the defender.
One of the TGW rules co-authors Rob Broom used to organise WW1 gaming days some years ago and there we used a house rule of using a pack of playing cards. A black suit for one side and a red suit for the other. The number of cards in the pack for each corresponding to the number of units each side had. You shuffled the cards at the start of each move and the moved/fired etc. each unit as yours or your opponents card came up. You could also opt to put a joker in the pack. When that was picked you just reshuffled and started a new move. If you had equal size forces, the attacker could also have 50% more cards than the units he had.
The rules worked a lot better using this rule IMHO.
I have since moved on to Bolt Action as they are a better set of rules in my view particularly as I believe Late War WW1 is better done at 1:1 to bring out the specialist roles of each of the platoon sections of the German, French and British armies at the stage of the war.
Bolt Action gets a bit too slow above two platoons though, so I am looking for ways to speed it up to cope with 1:1 company size games or find another set of rules I like as much that can cope with this size of game.