Trivial using a database

SELECT *
  FROM File1
 WHERE id IN (
           SELECT id
             FROM File2
       )
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But really, it's also trivial using Perl.

1. Load ids from second file into a hash
2. For each record of File1,
   1. Extract the id,
   2. If the id is in the hash from the second file,
      1. Print the record.

Either way, you read and process each line of the first file once, not once per line in the second file.