Alonso, playing in his 100th international, headed in Jordi Alba's cross for the opening goal after 19 minutes and clinched victory for the holders with a stoppage time penalty.
Spain now face a mouthwatering semi-final with Iberian neighbours Portugal in Donetsk on Wednesday.
"Xabi is a very good team player, he knows how to help on the flanks. He is one of the attacking strengths we have but overall it was the teamwork," Del Bosque told reporters after Alonso's 14th and 15th goals in international football.
"I think Xabi scores a lot. If we talk about Xabi and [Sergio] Busquets I think they are not too defensive. They know how to attack."
Spain fielded the same team that started against Italy in their opening Group C game, meaning forward Fernando Torres was on the bench.
Del Bosque's wisdom of playing without a designated centre forward has been questioned in some quarters but the coach made clear his reasoning for his striker-free selection.
"I don't think there is an absolute truth that playing with a true forward gives you more depth, but we wanted to dominate to have possession and create chances," he said.
Spain were too good for a meek French side, who offered little hope that they could continue their mastery of the Spaniards in competitive meetings having won five and drawn one of their previous six encounters.
"I don't think it is an unfair result. We were in control most of the time," said Del Bosque.
"We were strong on the left with Jordi and [Andres] Iniesta, that's where the first goal came from. We played well as a team and that's what caused France problems."
Del Bosque said Spain were at a "little disadvantage" with Portugal having an extra two days rest to recuperate before the semi-final after beating the Czech Republic on Thursday.
"We were tired at the end of the game but we will have to do our best to rest as much as we can," he added.
