185? Or 183? Can't Tell

Seeing that Napolean III did not start his reign until1848, it would have to be 185X.

This portrait of Napoleon III is bare-headed, and was issued 1852-1857. No coins were issued 1858-1860, and the portrait changed from bare-headed to wearing a laurel wreath in 1861. On that basis, I'd say this one is "1857".

Moving on to the mintmark, which is beneath the eagle. Sure looks like an "A" to me, which would be Paris mint, usually the most common mintmark.

What we can't tell from the pics is the denomination; I can see the middle of the word "centime", but not the denomination before it. The French Empire issued 1, 2, 5 and 10 centime coins all with an identical portrait/eagle design, and all four were issued in 1857 in Paris. The only difference is the size:
1 centime: 14mm
2 centimes: 19mm
5 centimes: 24mm
10 centimes: 29mm

The 5 and 10 centimes were often found in circulation in Britain, as they are the same size as the British bronze halfpennies and pennies; the smaller coins are less-frequently seen. But I don't know what's likely to turn up in the US. Based purely on mintages, the 5 centimes is most probable.