A few things would have needed to happen, and even still, the survival of a Blois dynasty would still be pretty iffy. Near the beginning of the Civil War between Stephen and Empress Matilda, Stephen had just defeated a Scottish invasion and was faced with Matilda and her followers arriving in England and based themselves at Arundel. Stephen had a chance to bottle up and capture Matilda then, but for whatever reason, he let her escape to Bristol, and that kicked off The Anarchy in earnest. Had he been able to capture Matilda, there certainly would have been a war, but Stephen would have had an enormous bargaining chip and possibly could have forced Matilda to recognize him as King of England.
Assuming war still breaks out, Stephen's son and designated heir Eustace of Boulogne, needs to survive. Perhaps with Matilda in custody, The Anarchy doesn't last as long as it did OTL, and Eustace died well towards the end of the war. His death really led to Stephen packing it in and recognizing Henry of Anjou as his heir while being allowed to remain king.
So Matilda gives up her claim to the throne and Eustace survives to succeed Stephen as King. However, the would-be Blois dynasty still has to deal with the very legitimate claim of Henry of Anjou, who would remain an extremely dangerous for for King Stephen (and subsequently, King Eustace), especially from all his Angevin holdings. Fortunately for the House of Blois, Eustace is married to Constance, sister of King Louis VII of France, so that's a potential ally for Eustace with which to further isolate Henry. In order for the Blois dynasty to really thrive, Henry has to be defeated and neutralized. If this doesn't happen, Louis VII ends up annulling his marriage with one Eleanor of Aquitaine. Though the circumstances are a bit different here, a marriage between Henry and Eleanor still makes a ton of political sense.
This would be an existential threat to the House of Blois and to the Capetians of France. Assuming the Blois/Capet alliance continues, then I have to imagine Henry tries to ally himself with the Holy Roman Emperor, who at this time would be the newly crowned Frederick Barbarossa, whose Swabian powerbase borders the French realm.
This feels like a giant powder keg. An awfully fascinating and truly intriguing powder keg.