Well, that’s not entirely true. The Celts originated in Central Europe (Germany, Austria, Switzerland), and migrated into Greece, Spain, and yes, into the British Isle. Although the falcata originated with the Iberians, the Celts living there which formed the Celtiberian culture would have used such swords. At least they have been found among Celtibetian archeological sites. Try googling Celtiberian culture if you want to learn more. It is still a subject of debate, but the Celts may have migrated into Spain from Central Europe before they headed to the British Isle, but this is still debated. At the very least, it was around the same time. So they may not have been a Celtic invention, but they definitely were used by Celts, or at least that is the consensus. And of course most know the falcata was copied by the Greeks, in the form of a kopis.
I’ve also reproduced Bronze Age Celtic swords similar to the one that had been found in Ewart Park, in the UK. I even work hardened the edges, as the Celts did. I attached a photo. Can’t entirely take credit for that sword though, as Neil Burridge cast the blade for me, but I finished it, did the work hardening, and riveted on the handle.
Ive also reproduced a few gladius, including two Pompeii and one Fulham, and I’m currently working on a second Fulham, with bone grip, and all. The earlier Roman swords such as the one in the picture do have a leafed shaped blade, which, as you mentioned was of Celtic influence. Later Roman swords ditched the leaf shape for easy of construction, as seen in the Pompeii Gladius.