The two parts of each Beattitude are: The conditions of the Blessing and the outcome of the Blessing.
I think Jesus wanted people to 'go deeper' than just to hear nice words. I think he wanted people to think and identify with what He was saying. The relationship of the Beattitude to the Fruit of the Spirit is the behavioural response of the blessed one of love, joy, peace, patience, kindness, goodness, faithfulness, gentleness, self control.