Your paternal grandfather was most likely of Berber origin. Some of them have married European women during past generations. Not only during French occupation but since times of Roman Empire and even before that. As a matter of fact a number of North African women look quite South European and genetically many belong to European mtDNA haplogroups. That is why your father has about 70% North African and 30% European blood, provided your mother is 100% European.
For digging further I would recommend you to order 67 markers at FTDNA and join a project maghreb.
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