So, to clarify, you want to find a bag that you can wear as a cross-body or as a shoulder bag?
Which flaps don't you like? That might limit the suggestions a bit
Of course there's the Natasha, which is a cross-body but I often wear it as a shoulder bag with the strap shortened all the way (I'm 5'5"). It's quite functional, and holds a good amount of stuff. I wasn't a fan of the style at first, but it's so easy to carry and I love the pleating on the bottom...so somehow I ended up with 3
There's the Lil Ukita, which has a long strap, shorter rolled handle, and a flap. I have the large one, and am a bit "busty" so I can't really wear it as a cross-body but depending on your body type, you can. The Lil Ukita is smaller than the Natasha and Hillier. The other two would definitely carry what you need (if by light sweater you mean a thin cardigan or something), but I'm not 100% sure the Lil Ukita would hold a sweater in addition to the other stuff you mentioned, as I don't have one. I did buy one once but returned it because it seemed so small to me. Maybe some other TPFers can post their opinions about what it can hold.
The Hillier is one of my favorite styles, and is definitely just a shoulder bag for me because the strap is pretty short, but again, might work for you as a cross-body. If you regularly only carry a wallet, phone, and keys, it would be too big for you but would suit your purpose if you needed to put other stuff in it.
Other options are the Aidan and Groovee, but I don't own these styles so I'm not sure how they would work as cross-bodies.
I don't have a Fran but I have a Francesca, the larger version, and for me it is not comfortable to carry on my shoulder (even when half-full), nor do I think it looks good carried that way, as the rolled handles are in the way or pull on the edges of the bag if they're hanging down. Based on what you usually carry, I agree the Fran might be too big, and some of these bags on their own can be pretty heavy.
