Comparing Days Sales

You need to change the syntax slightly:

Sales PY Parallel = CALCULATE('Sales Fact Table'[Total Sales],PARALLELPERIOD('Fiscal Calendar'[Date Field],-1,Year))

The -1 indicates the interval and you want Year instead of Month as your periods are a year apart.

I'm not sure if 'Fiscal Calendar'[Fiscal Period] is a date field, but the expression requires the field to be a date data type. Instead of the text string that presumably makes up 'Period 1', you could create a date column, if there is not one already, with values such as 01/03/2019 for '01/03/2019-27/03/2019', so that everything for that period is recorded on the first day of the month. Then you could use this field in the DAX expression - Having said this, this date field should allow you to use SAMEPERIODLASTYEAR.

If you don't have the date field already, you could extract this from the text string using LEFT (https://docs.microsoft.com/en-us/dax/left-function-dax) and DATEVALUE (https://docs.microsoft.com/en-us/dax/datevalue-function-dax)