Fred was named personally by Curt Connors after Fred Flintstone from the classic television show The Flintstones because other Oscorp scientists named Wilma after a different character in that show. He was captured specifically by Oscorp Industries scientists and is now a test subject to many of them. He quickly became a lab pet to Connors, and would endure most of his experiments.
His latest known test was when Connors injected him with the Lizard serum to see if he would regrow his lost limb; Peter Parker held Fred in his hands while Connors injected the mouse. Fred soon turned out to regrow a fourth leg, a result that was one of the most astonishing in all of Oscorp history. After this, the scene in the movie shifts from Connors' Oscorp lab to May and Ben Parker's house and it is implied that Wilma was injected with the same serum.
Unfortunately, the serum proved itself to be too dangerous, for the serum also affected the DNA with lizard cross species genetics. The serum not only enabled Fred with another limb, but also turned him into a hybrid mouse with reptillian scales and cold blooded personality. Peter found Fred in the lab, and found him eating Wilma, showing Peter what happened to Connors when Connors also injected himself with the same serum.