I receive files which names contain spaces and change every week (the name contains the week number)
IE, the file for this week looks like This is the file - w
First of all, you should not use the dollar sign in an assignment.
Moreover, wildcard expansion is not called in an assignment. You can use process substitution for example, though:
FILE=$(echo 'This is the file - w'*.csv)
Note that the wildcard itself is not included in the quotes. Quotes prevent wildcard expansion.