Marseille had to buy 46 pairs of new boots and even offered to charter a special flight to bring footwear from Portugal after the disappearance.
The Portuguese outfit left their boots in their dressing room at Marseille's Stade Velodrome stadium after training there on Wednesday night.
On Thursday there was no trace of the studded footwear.
"There is nothing which allows us to contradict the Portuguese officials' version of events," a police spokesman said Friday.
The match went ahead with the French team triumphing 1-0.
Some of the Braga team used reserve pairs of boots which they had brought with them and left at their hotel. Others had to use the new boots bought by Marseille.
"I find this incredible. No door had been forced, how did the boots disappear?" said Braga's president Antonio Salvador Rodrigues on Thursday.
Braga have registered an official complaint with police, who said an investigation is ongoing.