Many historians of repute...and charlatans!...have contended that those who can claim a descent from a "gateway" ancestor can in turn trace or plausibly speculate upon a line that stretches back to classical civilization. Such a line is called a DFA one, or "Descent from Antiquity".
While there are a few alternative candidates, the ancestor most likely to be traced from one who has Western European ancestors is the famous Emperor of the West, Charlemagne. Using the most conservative theories, such as those put forward by the respected Christian Settipani, I've submitted a possible line of ancestry from Charlemagne to Amyntas of Macedonia, continuing in a principally legendary/mythical one to Herakles (Hercules). Females are in CAPS.
1. Charlemagne (d. 815)
2. Pepin the Short
3. Charles Martel (the Hammer)
4. Pepin the Fat
6. Arnold of the Riparian Franks
7. Bodigisel II
9. ARTEMIA OF LYONS
11. Ruricius (Bishop of Limoges, d. 501)
12. Hermogenianus Faltonius
13. Adelphius (Bishop of Limoges, b. ca. 390)
14. ANICIA FAUSTINA PROBA
15. TURRENIA ANICIA JULIANA
16. Anicius Aucherius Bassus
17. Amnius Nicomachus Anicius Caesonius
18. Amnius Anicius Julianus
19. Sextus Anicius Faustus Paulinus
20. ASINIA JULIANA NICOMACHA (fl. 215)
21. Caius Asinius Nicomachus Julianus
22. Caius Asinius Quadratus Protimus
23. JULIA QUADRATILLA
24. A. Julis
25. JULIA QUADRATILLA
26. IOTAPE (Princess of Commagene)
27. Antiochos IV (King of Commagene, d. >72 CE)
28. Antiochos III
29. Mithridates III
30. Antiochos I (King of Commagene, d. 36 BCE)
31. LAODIKE THEA
32. Antiochos VIII (King of Syria, d. 96 BCE)
33. KLEOPATRA (Princess of Egypt)
34. Ptolemaios VI (Pharaoh of Egypt, d. 145 BCE)
35. Ptolemaios V
36. Ptolemaios IV
37. Ptolemaios III
38. Ptolemaios II
39. Ptolemaios I (Pharaoh of Egypt, d. 283 BCE)
43. Amyntas (Prince of Macedonia)
44. Alexandros I
45. Amyntas I (King of Macedonia)
48. Philippos I
53. Karanos (legendary first King of Macedonia)
63. Herakles (Hercules)
Further, Hyllos's mother was DEIANEIRA, whose mother was ALTHAEA, whose father was Thestios, whose father was Ares, God of War.
Thanks for a lively and entertaining post, Batrochides. I don't think I'm descended from Hercules. Morgan le Fey, perhaps, but not Hercules.
It's nice to see you around. I wish you'd drop by and do an historical or mythological thread more often.
Be well and happy.