Something that's a float is not an int. They're separate types. You can have a float that represents an integral value, like 1.0, but it's still a float.
(Also, user_input == int isn't checking whether user_input is an int, it's checking whether user_input is actually the type int; you wanted isinstance(user_input, int). But since that still won't work, let's skim over this part…)
So, can you check that a float has an integral value? Well, you can do this:
if int(user_input) == user_input
Why? Because 1.0 and 1 are equal, even though they're not the same type, while 1.1 and 1 are not equal. So, truncating a float to an int changes the value into something not-equal if it's not an integral value.
But there's a problem with this. float is inherently a lossy type. For example, 10000000000000000.1 is equal to 10000000000000000 (on any platform with IEEE-854 double as the float type, which is almost all platforms), because a float can't handle enough precision to distinguish between the two. So, assuming you want to disallow the first one, you have to do it before you convert to float.
How can you do that? The easiest way to check whether something is possible in Python is to try it. You can get the user input as a string by calling raw_input instead of input, and you can try to convert it to an int with the int function. so:
user_input = raw_input("Please enter a multiplier!")
try:
    user_input = int(user_input)
except ValueError:
    print " Please enter a number"
If you need to ultimately convert the input to a float, you can always do that after converting it to an int:
user_input = raw_input("Please enter a multiplier!")
try:
    user_input = int(user_input)
except ValueError:
    print " Please enter a number"
else:
    user_input = float(user_input)