Their quality of life has improved dramatically since they moved to France.
Their quality of life improved dramatically when they moved to France.
Are both interchangeable?
YES.
#1. suggests that they still enjoy the improvement in quality of life now.
#2. suggests that they enjoyed the improvement in quality of life at the time of moving to France, but it is unsure whether or not the effect of the improvement has lasted up to now. They may get in a miserable state now again.
Touche, Haihao.