May I congratulate you on choosing an *excellent* name for your bird! My Dad was Francis (Frank) and my sister is Frances (Francie). I have two(2) statues of St Francis, a big one in my yard and a smaller one in the hallway. The thought of having a bird called Francis makes my heart go all smooshy.
Y'know what? We all want to live in peace and harmony with our companion animals around us and, hopefully, all getting along like a house on fire. Sadly, though, it's not always possible. Sometimes, you can make things work and sometimes just not. When we lived at our old house, my Beaks had the run of the place and had strategically-placed perches in every room so they could fly around at will. Cats and dogs were in the house too, but none of them ever raised an eyebrow at the birds 'cause they were up high and the animals were on the floor.
This new house has big windows and is a much lighter, airier place. The animals notice the birds flapping about now and the birds are far more likely to land on the floor (an absolute deal breaker AFAIC). I cannot have the birds and the animals about in the house at the same time. This means three cats and a dog have to be sent outdoors when I've got the birds out. That's just the way it has to be. I cannot risk the wellbeing of any of my creatures and so I do what I must to prevent that one freakish accident that could happen if I allow them in the same space together.
Just *one* time, one of the Beaks landed (by a dreadful error of judgement) on top of our old dog's head. God bless Alice: she just stood there, thinking 'What the...!?' I was quick enough to whip Barney away, but that one incident highlighted the possibility of a bird landing, digging claws in for stability and the dog (or cat) whipping round and... well, you can guess the rest. So, never again for us. I keep them separate.
Whatever Francie's reason is for hunting after your cats, it's his and he means it! If he bites or claws a cat and it (quite reasonably) retaliates, the aftermath could be a terrible tragedy. I'd keep them all separate, even if it means making major changes regarding who sits where or which room the bird and cats are allowed in. I know it's not a set-up that you'd want, but it's probably the most sensible.
PS. Rosetta sends a happy screech to her new friend, Francis!