Mott had previously been spotted in Pennsylvania.
When Mott and French did not pick up the teenager's father on Wednesday, the couple returned to their home via Uber and found it looted.
The Neptune Beach Police and the Jacksonville Sheriff's Office - where Mott's father works as a correctional officer - launched an investigation that uncovered "possible criminal violence inside the home", CBS reported.
Earlier this week, the mother of the missing teen, Carrie Campbell-Mott, issued a plea to the public for the pair's safe return on social media and a Florida Missing Child Alert was issued for Mott on Tuesday. 'No matter what, Logan is our child and we love him...
The deputies also said they had obtained an arrest warrant charging him with stealing his grandmother's vehicle and that he was a "person of interest" in her death, according to the paper.
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Trump came out against the measure as president-elect and said that the USA should use its veto power on the U.N. The resolution later passed after the Obama administration said it would not use the veto power.
Mott is considered armed and risky.
Police investigated at two locations Thursday and Friday - French's home on Nipigon Avenue South in Mayport and Seagate Avenue in Neptune Beach.
"My girls go to school right here at the high school and they're always in the neighborhood walking around so it was sort of chilling", neighbor Laura Taylor-McGhee still trying to understand what happened. "Mom", Campbell-Mott said in the post.
Her son, Campbell-Mott wrote, was good and kind to his family. Please call me. I will help you. It was just a normal conversation'.
He was detained near Buffalo, New York.