Water pressure from slope causing crack and lean in foundation. Is a French drain the answer?
A French drain needs a location to drain to. Some drains are like a curtain in front of the house that extend down the side of the house to the lower area where the water can drain. If there is not a way to move the water or allow it to flow it would be useless.  Some drains on flat ground end up in sumps so the water can be pumped out. Most of my homes have been in areas that had a slope and I have installed them to drain water coming down the hill to the house and causing foundation problems simple 3’ French drain with pipe in the bottom extending to the low side of the house eliminated my problems, other homes deeper drains were needed but that property had a huge slope. After the drain was added the problems were fixes at that place. It looks like you have a fair drop to the property behind yours as the roof level looks to be almost at your ground level so you have 5-6’ of slope to work with if that is your yard, put the drain in the front drain to a low side or if level side to side both sides to the lower area in back, this should help if surface water coming down is the issue and this can cause problems with only a few feet of slope. The good news a small slope of only a couple of feet usually only requires a trench 18-24” deep, I find steep properties require deeper trenches , my last home had 5-1/2’ deep ~10’ in front of the house and that set of drains below the house we had to bring in more rock as it flowed like a fire hose ok no pressure but but the 4” pipe was flowing almost completely full of water, flowing onto rock we dumped. The drain helped in several areas of that property.