digging french drains

hi folks,

My intention was to rotovate the whole back garden and re-seed but we had a bit of flooding and I think it would be good to try cure it before I grow new grass

I'm not really pushed on the whole idea of getting a mini digger in and digging huge drains the length of the garden.Nor am I keen on the expense of pipes fabric etc so.

I am thinking of hand digging a 7 meter trench 12inches deep and 10 inches wide and filling it with hard core before back filling

I might also dig a few sink holes in the worst spots and fill them with hardcore too.

Would this do the trick ?

Should I rotovate first to make digging easier btw ?

Thanks