Euchre tournaments come in two genuinely different shapes: fixed-partner knockout (this bracket) and progressive euchre with rotating partners (a score sheet, honestly — see below). Both are covered here, including which tool fits which night.
fixed-partner knockout or round robin
Teams of two stay together all night and play a single or double elimination bracket. Standard match: first to 10 points, or best two of three games to 10 for later rounds. Eight teams (16 players) in single elim is 7 matches — a clean card-night. Sixteen teams runs a full evening.
Double elim is kind in euchre specifically, because the deck has opinions: one cold run of hands should not send a team home at 7:45.
For a club night where everyone should play everyone, use the round robin format instead of a knockout: each pairing plays one game to 10, the W/L grid keeps standings, most wins takes the night. Six fixed teams is 15 games — likely two evenings; four teams is 6 games, one evening. Tables run in parallel, so even-numbered fields keep every table busy.
Progressive euchre (rotating partners, winners move up a table, score accumulates individually) is the most popular home format — and a bracket is the wrong tool for it. There are no fixed teams and nobody is eliminated; what you need is a tally sheet per player and a bell. Run progressive on paper, then use this bracket for a championship knockout among the night's top 4 or 8 scorers, which gives the evening a proper final hand.