G'day,
I'm not very familiar with the Second Empire, but I have a copy of Gadoury's excellent catalogue.
The 1, 2, 5, & 10 centimes are all bronze, and visually, they are very similar. The denomination is in text at the lower edge of the reverse.
When you say the diameter is "15cm" (~6 inches), I suspect that you meant to say "15mm".
Which is the diameter of the "un centime" from 1853 to 1870.
I can't make out the date in your pic, but you say it's 1854. In that year, 1c was minted with the following mintmarks: A, B, BB, D, K, & MA. The mintmark is immediately below the eagle's feet. From the prices in Gadoury, the mintmarks seem almost equally common, except that D has a bit of a premium, but B has a big premium. Curiously, the mintages aren't all that different. Yours looks like a D (Lyon):
1,545,967 minted;
grade "B" ~ 10 euros. Your pic looks like a Bminus to me, because not all of the legend is readable.
Peter in Oz