I'm afraid that doesn't seem possible...
The House of Burgundy, the first royal house of Portugal, was a cadet branch of the Capetians. However, they were relatively distant...
Alphonso I of Portugal was the son of Henri, 15th Count of Portugal. Count Henri was himself the youngest son of Henri of Burgundy, the latter being the son of Robert I, Duke of Burgundy. As for Robert himself, he was the son of Robert II of France, and thus the younger brother of Henri I of France.
To sum up, here is the simplified genealogy :
ROBERT II (972-1031) King of France 996-1031
=> HENRI I (1008-1060) King of France 1031-1060
==> Four children, including his eldest son and heir Philip I
=> ROBERT I (1011-1076) Duke of Burgundy 1032-1076
==> Henri of Burgundy (1035-ca.1074)
===> HUGUES I (1056-1093) Duke of Burgundy 1076-1079
===> EUDES I (1060-1103) Duke of Burgundy 1079-1103
====> Four children, including his eldest son and heir Hugues II
===> HENRI (1066-1112) Count of Portugal 1094-1112
====> ALPHONSO I (1109-1185) King of Portugal 1139-1185
If you wished for a personnal Union of France and Portugal, you would have to kill every descendant of Henri I of France and Eudes I of Burgundy. Problem is that by 1139, there are already a lot of them :
-In 1139, the King of France is Louis VII, great grandson of Henri I, and he has four brothers (including a bishop and an archdeacon). Not to mention that his father, Louis VI, wasn't the only son of Philip I who himself had one brother.
-As for Burgundy, the current Duke is Eudes II, grandson of Eudes I, who has no less than five brothers alive.
And that's only without including female lines, as the French Salic Law worked. But that law didn't exist in 1139 as it wasn't used before 1316 : it can thus be argued that it wouldn't be applied. This would include a LOT more people.
Thus, chances of Alphonso I or one of his descendants getting the crown are very VERY slim.
Not to mention that the Houses of Aviz and Braganza are both illegitimate branches. They got the throne of Portugal thanks to special circumstances (the Avizs to prevent a Personnal Union of Portugal with Castille, the Braganzas after a rebellion against Philip IV of Spain), but their illegitimacy got rid of what little rights they could have had on the French throne.