In Bash:
var=$(printf 'FILE=_%s_%s.dat' "$val1" "$val2")
or, the equivalent, and closer to sprintf:
printf -v var 'FILE=_%s_%s.dat' "$val1" "$val2"
If your variables contain decimal values with leading zeros, you can remove the leading zeros:
val1=008; val2=02
var=$(printf 'FILE=_%d_%d.dat' $((10#$val1)) $((10#$val2)))
or
printf -v var 'FILE=_%d_%d.dat' $((10#$val1)) $((10#$val2))
The $((10#$val1)) coerces the value into base 10 so the %d in the format specification doesn’t think that “08” is an invalid octal value.
If you’re using date (at least for GNU date), you can omit the leading zeros like this:
date '+FILE_%-m_%-d.dat'
For completeness, if you want to add leading zeros, padded to a certain width:
val1=8; val2=2
printf -v var 'FILE=_%04d_%06d.dat' "$val1" "$val2"
or with dynamic widths:
val1=8; val2=2
width1=4; width2=6
printf -v var 'FILE=_%0*d_%0*d.dat' "$width1" "$val1" "$width2" "$val2"
Adding leading zeros is useful for creating values that sort easily and align neatly in columns.