Care ofPrisoners of Warfrom whatever service came under the Admiralty. Prisoners sent to Oswestrywere parole prisoners [mostly Commissioned Officers] and the first batch were sent from Okehampton in December 1811.
Registers of prisoners are in document series ADM 103 = Records of Medical and Prisoner of War Departments; Navy Board and predecessors: Prisoner of War Department and predecessors: Registers of Prisoners of War.The records usually give detailed descriptions, with the places of birth, and should show circumstances of the capture and the ultimate disposal of the prisoners.
The majority of the Registers consist of the General Entry Books kept by the those in charge of each prison hulk, depot or parole town. They contain many lists of prisoners, usually arranged by nationality or by place of confinement or parole. This makes searching for a prisoner a difficult task, luckily you know your looking at Oswestry.
A search of the catalogue [PROCAT] at http://www.catalogue.nationalarchives.gov.uk/http://www.catalogue.nationalarchives.gov.uk/ reveals two sets of records in the National Archive, Kew [searched forprisoners AND oswestry, 1810-1820]:
ADM 103/594 Parole Prisoners at Okehampton and Oswestry. 1809-1812 and ADM 103/595 Parole Prisoners at Okehampton and Oswestry. 1815.
The records are not available to search online but you can order a copy of the relevant pages for the Paris names, visit the Kew in person or use a researcher.
There are many more records covering the same period [search prisoners of war 1810-1820], but I suggest you look at the NA research guide "Prisoners of War in British Hands: 1698-1949(Ex-PoWs and Displaced Persons, 1945 onwards)" available online [from Catalogue home page select "research guides".
There is also an article of the South West Maritime History Society giving some background to the transfer to Oswestry that may be ofinterest seehttp://www.swmaritime.org.uk/article.php?articleid=31&atype=a
It's also possible Shropshire Archives or Oswestry Library could have information relating to the parole prisoners, both have web site for contact details.