In the 2005–2006 season, Hesperange finished ninth in the National Division.

The following year, they improved this position to fifth, level on points with fourth-placed Racing FC and sixth-placed CS Grevenmacher.

The gained promotion back to the top division in the 2019–2020 season where they finished third in their first season back and qualified for play in Europe.

Overall, Swift's record in European competition reads: Note: Flags indicate national team as defined under FIFA eligibility rules; some limited exceptions apply.

Note: Flags indicate national team as defined under FIFA eligibility rules; some limited exceptions apply.