Just take an old multimeter, or a free one from harbor freight... or any type of device which uses batteries or even those battery containers ( you can buy these from Amazon, eBay, and elsewhere - small self-contained boxes which can house batteries and plug into a socket )...
Desolder the piece of metal and solder it to the sheet metal. You can lift those out of those grooves. Take it out so you don't melt the plastic. You don't need to pull it all the way out - but take all the batteries out. It doesn't hurt to clamp a heatsink to it in the form of simple vice grips or needle nose grips... a few inches from where you want to solder so the heat doesn't go beyond that, but not so close that most of the heat immediately dissipates into the grips.
Then, tin the metal, and make sure it will fit into the area... then tin the spring bit... this helps because the solder will be easier to heat up on each individual piece and it will stick to one another without having to heat the spring bit up super hot... although once it is connected - using tweezers you'll want to heat up the spring a bit so the solder flows through and makes a solid connection which won't go anywhere. You can also stretch it out so a small piece of the wire is what makes the connection.
If you don't have a soldering iron - you can buy a T12 soldering iron ( KSGER ) from AliExpress or whatever it is called, for like $20 to $50. 2.1 or 3.1 should be fine. You can get the mini one, or the full size. The blue plastic one with the black cover and no screw cap is pretty good to use. Doesn't heat up in the hand, the tips are easy to replace, etc... You can get the kind which uses the 24v 3 or 4 amp adapter, or the kind which has the power supply inside the unit. Either will work - I would recommend a few mods to the unit but for this quick thing it would be fine.
You could also drill a hole through the piece of metal in your fluke, and a hole in a flat piece of spring plate and connect them with a small screw - or even solder through that... You could use a simple mechanical crimp without using a soldering iron too but you may lose power as it oxidizes over time.
There are so many options available - most of them are under $1 completed. Many under $5. If you have a soldering station then just salvage a spring in the form of a battery spring or the flat spring type - whichever was on your unit - and attach it with solder. You can also drill a hole which will help heat the area up quicker and having a solder blob go through both pieces will aide in the connection. If you use a spring plate, attach a vice grip to the spring face - not sure if the spring will lose its springiness if you heat it so having the vice grips will prevent heat from getting too hot up in that area... it will make it harder to heat the bottom part up so heat furthest away...
Avoid cold soldering - ie: don't put solder on the tip and then drag it off onto the metals as that won't actually bind to the metals. You want to ensure the metals are hot enough that the solder wire will flow onto them... ie: you should be able to take the solder wire and touch the piece of metal you want to solder and that piece of metal should melt the solder... not the soldering iron tip. It doesn't hurt to put a little bit of solder on the tip as this can help with heat transfer - but don't flood the tip as flowing from the tip to the metal usually leads to a bad joint. you want the metal / wire itself to be hot enough to melt the solder.
whether you use a mechanical connection or soldering - both will work.
If you do drill a hole in both.. You can make a hole in one, then use a hole punch or a crescent punch to cut the hole with a mallet / hammer and push it through the hole in the other piece. You can do this to create a rivet. You can also use an actual rivet to attach the metals. Then you can hammer them thin.
There are many many many ways to fix this issue. You can also contact fluke to see if they have that piece of metal as a replacement. If they do not, you can find someone to make it by measuring how long it is in each direction, which folds, etc... - they are not complicated. You can make them yourself too using a pure nickel roll of metal. You can also use plated, but pure or close to pure is better. But you have a very small issue - you don't need to go this route.
Just get a battery holder, or salvage the spring you need off something... or if you have the one that fell off this unit - just solder it back if you can't rivet it... ie if it cracked along the edge or something then soldering would work really well. just remove the piece from the plastic.
IF you are in North Carolina - near Asheville... I could fix this for you if you bring it by. just bring the entire thing and any pieces which fell off. shouldn't take more than a few minutes and I wouldn't even charge.
Edit: Yeah - spot welding would also work if you have the full spring, but those can come off over time. Solder joints can crack too if the connection isn't that good and isn't fully wrapped, etc... Spot welding usually survives for a long time though. You would need enough material - you could do it along the edge... You could also spin weld it across an edge which wouldn't even melt the metals, technically... and the metals wouldn't lose their characteristics if done properly. It is how rockets are assembled. Quite fascinating actually.
So yeah... you have plenty of options available. You can make a spot welding tool just by using a battery, 2 contacts, a switch between ground and positive. I would recommend using youtube to look up how to make one.... then tap the button. That would create a short and weld the pieces by getting really hot for a very very short amount of time so you wouldn't even have to worry about the plastic melting, etc... If it cracked and you have to spot weld the edge... start on one edge and get it aligned and hover the contacts ( 1 on top, 1 below - best to tape them close together so the metal can slide between easily ) and then tack it on one side, then the other... then do all the way in between. Then you put a bolster on it with thin nickel sheet...
plenty of options. and can be done very quickly / easily.