I can't get my bike to turn over, I get ra ra click click click. The battery is brand new and reads 12.56 volts on multi meter. I checked all the connections and all are tight and clean.
The thing making the clicking noise next to the battery (battery relay?) I thought I replaced not too long ago so I can't figure out what it could be.
Short version:
I think your starter's brushes may be worn or at least sticking, unless the battery is just not up to the task of turning over your engine.
Long version:
On your 2003 FSE400, the starter was still located in the forward location. This lets the starter take the first (and every) splash hitting the engine when you launch into a mud hole or creek crossing. (This was changed on the 2005 models, when the GG engineers moved the starter around to the rear of the cylinder.)
During research, I found that the original GasGas starter is a Yamaha spec starter that has been modified. The connectors run out the end of the starter housing, instead of the original Yamaha location on the side. My 2003 FSE400's starter had a rubber plug over the original hole in the case, and it proved completely inadequate to keep water out of the starter during deep water crossings (and muddy water out during deep mud hole crossings).
Also, the exhaust cam that came on my 2003 FSE did not bleed off enough compression during starting. Until I upgraded the "starter to starter clutch" gear assembly and installed the upgraded (properly working) 2004 exhaust cam, the battery of my bike wouldn't properly roll over my engine. For the first year I owned the bike, I actually had to kick the start lever and push the starter button at the same time to get the bike to start. (I also had to replace, under warranty, my backfire induced trashed starter clutch.)
All this extra work that my starter had to do was hard on it's brushes.
I had a friend at a local automobile starter repair shop replace the brushes in my starter and clean out the mud and moisture twice; and also repair the starter of several of my FSE owning customers. (He replaced them once and the other time, he just reshaped the brushes and re-soldered the connecting wires after he cleaned out the muddy gunk that was not allowing the brushes to move freely.)
I would obtain the proper square/flat shaped o-rings to replace those on the starter body, so that it would seal after the job was performed.
I would also, while the starter was disassembled, remove the rubber plug in the housing, and holding a thick paper inside for a form, permanently plug the above mentioned un-needed hole with "QuickSteel". (Now it's sold as J&B Weld. You know the stuff; it comes as a two layered stick in a clear plastic round tube.)
After these upgrades, my starter worked just fine. The bike was great. I made several KTM 4-stroke owners feel bad, when I honked the horn before I passed them in the tight woods. That bike sure dodged trees well.
OMT... Once, I heard that clicking noise you spoke of. It was the relays. My battery tested "good", so I purchased and installed two new new relays. It still clicked. I then installed a new battery. After installing the new battery, the clicking stopped, and everything then worked properly. I took out the new relays, and reinstalled the original relays. They also worked perfectly, with the new battery. (I still have the replacement relays, for sale, in my inventory, as well as some of the square bodied o-rings for sealing the housing.)
In your case, if everything else was good, I would take the electric starter apart, and then clean and inspect the brushes (and seal the rubber plugged hole).
Note: Be careful to not let the connector post (protruding from the starter) rotate when you are disconnecting the leads (wires). When the starter was modified to have the connector post come out the end, the starter housing no longer had the "cast in" connector post retainer in the correct position to keep it from rotating as one connects or disconnects the wires. If the post rotates, it can rip out the wire that connects it to the brushes. (See the part above where my starter repair man had to resolder my brush's connector wire. I learn by experience really well.

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Stocker Starters was as big a help to us at Smackover Motor Sports with starter components as the GasGas suppliers were. Elwood Stocker is the Man! (He probably won't have the modified starter housing in stock, but will have an almost identical starter in stock. One would have to swap out that part of the housing with the original one, on their pre-2005 FSE.)
I hope that some of my ramblings have given you an idea as to what to look for to cure your problems.
Good Riding and Wrenching!
Jim