First of all, the Baron is different from the one in The Cat Returns, except that the voice of the cat is from the same person.
The Baron statue has a story to it that Mr. Nishi tells Shizuku Tsukishima. The Baron statue had a female statue that went with it. One day, the female statue needed to get repaired. Mr. Nishi sees the baron statue at a cafe in Paris, France with a lady named Louise. The owner agrees to sell, and Louise would give Mr. Nishi the other statue when it's repaired.
Mr. Nishi returns to Japan, but then WWII broke out, and he never saw Louise again. He does go back to Paris, but he never saw her. Shizuku Tsukishima uses the baron statue in her story called Whisper of the Heart.