"She likes those rocker types. They have mutual friends and just met through hanging out," a source said.
The new couple stepped out publicly for the first time when they visited the Apple Store in LA, reported Us magazine.
After splitting with "Step Up Revolution" director Speer in December 2011, Tisdale, 27, briefly dated Boys Like Girls musician Martin Johnson.
The romance quickly fizzled and the "Scary Movie 5" actress reconciled with Speer, 30, in May.
"Ashley and Scott split for the same reason they did last time. Their relationship just ran its course," the source added.
Prior to dating Tisdale, French was linked to 'Big Bang Theory' actress Kaley Cuoco.
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