Milk frothing is an interesting area. I own several units.
Obviously with an espresso maker you can froth milk. As you are talking French Press that is not likely an approach for you. I own the Froth Au Lait. Does a wonderful job but work to set up and clean.
Also there are simple plunger units. Actually work quite well.
Bodum makes one but it is not cheap and quite fragile. This one is a low cost knockoff. I have both types and find they do the same job.
Personally I mostly use a hand blender.
The factors I find important is the type of milk and if you heat it. I did some experiments on using cold vs heated milk. Cold milk frothed better but the froth almost instantly disappeared when added to the hot coffee. Frothing hot milk is more work but lasts when added to the cup.
I use a combination of evaporated milk and 10% fat light cream. The evaporated milk helps in the frothing. The more fat in the cream the easier it is to froth. I microwave the mixture then whip with my hand blender.