You can pause time while fishing by clicking on the journal icon. Fish will still bite while the journal is displayed; simply click on the screen (outside the journal) when a fish bites to close the journal and begin reeling the fish in. This exploit does not work by hitting the "F" key.
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* Opening the journal by clicking on the journal icon while fishing pauses time, but fish still bite while it's open.
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This works on Xbox as well; use the right stick move the mouse over to the journal icon, press A to enter the journal, then press B followed by X when you hear the bite sound.