Siege of Bethune, July 15 - August 29, 1710

Siege of Bethune, 1710
Engraving by unknown author
(British Museum, link)

French garrison of Bethune was under Governor Lieutenant General Antoine Le Prestre de Vauban, Comte de Puy-Vauban. He was the nephew of the "Great Vauban". Under his command also served Marechal de camp Michael Roth, Brigadiers de Mony, du Thil & de Saint-Sernin. The garrison was about 4,000 men:

Source: Pelet & Vault. Mémoires militaires relatifs à la succession d'Espagne sous Louis XIV. T. 10. P. 295.
Allied forces under General-Lieutenants Johann Matthias Graf von der Schulenburg (of Saxon service, commanded Imperial troops) & François Nicolas Baron Fagel (of Dutch service, commanded British-Dutch troops) totaled about 30-32,000 men:

Source: Feldzuge des Prinzen Eugen von Savoyen. B. 12. S. 609.

Bethune finally capitulated on August 29, 1710 on the terms of the free passage of the garrison to Arras. French lost 435 killed & 800 wounded (according to Puy-Vauban's Relation). Allies lost 854 killed & 2507 wounded.
The detailed account of the siege you may find in  J. P. F. Reeve's "The Siege of Bethune 1710: The Journals of Private Deane and General Vauban Compared" (you may reed it on-line at JSTOR: link)