For which part? You have booked an I fare, so the longhaul segments book in to I class. The European connector is booked in to J as per the fare rules, and any US connections will book in to I, A, or Y as per the fare rules.

For a 3 class aircraft (AA or US) this will mean you will book in to business class.
For a 2 class aircraft (AA or US) you will fly in first but either be booked in a business fare bucket (typically only offered on BA codeshares) or a first fare bucket (as AA/US do not offer I fare bucket on 2 class aircraft).
For a 1 class aircraft you will fly in economy.

Also note that although the European component is booked in J, it is not fully flexible. Your underlying I fare ticket rules apply.