Question

Francis had a lot on his mind that afternoon, he was concerned about his mother’s illness and about losing his job.
Is this correct punctuation

Answer 1

I wouldn't say it is correct. 
The correct version could be:
Francis had a lot on his mind that afternoon - he was concerned about his mother's illness and about losing his job. 
Or:
Francis had a lot on his mind that afternoon; he was concerned about his mother's illness and about losing his job.