FCFE: debt paydown

"Although the FCFE declines in the year when debt is paid down, it will increase in subsequent years."

Correct.

FCFE↓ = NI + NCC + Net borrowing↓ - NWCInv - FCInv

In the later years, however, it will increase because of the reduced interest expense(e.g. higher net income); thus, a higher shareholder value.