The Jay Treaty was no more an alliance than any other treaty we signed at the time.
Not true. None of the other alliances gave preference and exclusivity clauses for the West Indies trade.
The Jay Treaty's date - 1796 - also places it smack in the middle of the "Napoleonic Wars" era - the period of nearly continuous hostility between Britain and France lasting from the start of the French Revolution and subsequent war in 1792 to Waterloo in 1815.