The birth of a Frederick Arthur Biddle was registered in the Barnstable district, June 1889, Volume 5b, Page 458. In order to get confirmation of his parents you will need to order a copy ot the certificate, quoting that reference.
I cannot see a Frederick Biddle in the Barnstable area in the 1891 or 1901 census, but there is a death registered in the Barnstable district, March Quarter 1890, 5b, 398, age 0, so I expect he did not live until a census.
In 1891 Frederick & Jessie Biddle were living at 8 Princes Street, Barnstable with son Percy whose age is unclear but I think is either 12 weeks or months. however I cannot see a birth registration for him.