Sort data frame by character and date columns

I'm trying to sort a simple dataset by a character column (descending) and a date variable (ascending).

   fx_code  date    fx_spot 
1      AUD 2000-01-31  0.6370  
2      AUD 2000-02-29  0.6178   
3      AUD 2000-03-31  0.6071   
4      AUD 2000-04-28  0.5839   
5      AUD 2000-05-31  0.5725   

When I run the following code

DF$date <- as.Date(DF$date, format = "%Y-%m-%d")
DF <- DF[order(DF$fx_code,-DF$date),] 

I am getting the following error:

Error in -.Date(DF$date) : unary - is not defined for "Date" objects