I have a Francotte SXS that has an object, likely a piece of broken off solder, rattling under the rib. While the rib is sound, not separating and rings like a tuning fork when tapped, it is somewhat noticeable when shouldering the gun or tipping the gun up or down at an angle given it moves up and down freely. Is there an easy fix. Any suggestions or recommendations?

Are you able to screw out the front bead sight and if so is the sight retaining hole drilled right through the rib into the cavity between the barrels. It maybe possible for the loose object (piece of solder) to sit under the hole and be pinned by inserting a sharp ended pin held down by the threaded front bead or even a good squirt of RTV sealer down the hole and allow to set to hold the object in place?

Failing that carefully listen to how far down the barrel cavity the object will go and then drill a small centred hole in the top rib at that position to allow a pin and blanking screw to be used or again RTV sealer to set and hold the object in one place. Allowing clear sealer to come level to the top of the drill hole would also be hardly noticeable without threading the hole or using a blanking screw.

If the sound can be traced to the area between the muzzle and the fore arm lug, drill a small hole in the under rib just in front of the lug. Introduce some thinned epoxy into the hole. Plug the hole and let set with the muzzle up. The loose chunk will fall to the bottom and get stuck in the epoxy. If the front bead can be removed and the loose item can be seen through the bead hole, same process applies.

Rattling under ribs is, most often, loose solder and I'd not worry about it.

However it can also, less often, be something worse such as a scab or rust of loose pieces of rust. Indicating that water has got under the rib and thus the barrels are rusting from the "hidden" part between the top and bottom ribs.

I'd certainly NOT start drilling holes in ribs as that can cause all sorts of problems.

The only true fix is to have the bottom rib relaid.

Is there anyway to apply heat to melt the solder (assuming it is in fact solder) without separating the rib? Its actually an interesting problem.

If you can get the annoying little blob of solder to settle in one spot and you know where that spot is,,it's possible to heat that area of the bbls & rib(s) and melt the piece.
It'll flow in with the existing tinned areas of the bbl and ribs inside the void.
BUT you have to carefully clamp the bbls & ribs up to avoid any movement when doing this.
You watch for the existing solder joint of the rib to brighten which means it's melted and that's all the heat you need.
Easy to do,,also easy to get in trouble if you don't know what you're doing.

Sometimes you can get the little roller to rattle it's way to an existing weep hole or site bead hole already drilled into a rib.
If you can,,and it's a frustrating job to do,,,it usually won't fall out thru the hole but it'll settle into position over the hole & block it.
Then a quick touch with a torch flame will melt it in the same manner as above. If you're fast, no clamping of the ribs is needed.
You may have to clear a threaded sight bead hole afterwards but usually not.

If you can be sure it's rolled and rattled its way all the way to the muzzle end and is up against the soldered up muzzle void between the bbls, resoldering that void will consume it in the process.
An electric soldering gun can be used for this and no clamping needed.
Since you have to do the work w/the muzzle down to keep the offending piece down against the muzzle solder an electric soldering gun or iron actually makes easier work of it in filling the void.

I've seen super glue used to capture and silence annoying solder pieces inside the ribs. A suitable amount pumped into the void through a site bead hole or weep hole,,then the bbls rocked back and forth so the ball & glue mix it up. Then set the bbls on end (pick and end) and let it set up for a day or so.

High temp wheel bearing grease injected w/a syringe was used by an old gunsmith I knew back when.
The solder ball just kind of stuck to the grease inside the void and silenced it.
He said the high temp grease wouldn't get runny when the bbls got hot!