1. It immediately achieves the great strategic goal of driving every overseas French colony into the hands of De Gaulle, avoiding thousands of allied deaths in the campaigns to secure the French Empire. Vichy France is occupied years earlier.
2. The Spanish and Portuguese governments collapse. Either they are replaced by puppet regimes which formally join the Axis, requiring massive amounts of German support to function, or they briefly join the Allied cause before being overrun. Whichever happens, Iberia probably becomes a latter day Spanish Ulcer to rival the partisan movements of Yugoslavia.
3. Mussolini and the pro-German fascists are absolutely humiliated; not only has he failed to secure Italy any of its territorial ambitions but its supposed ally has set out to annex its existing empire! Italy begins looking for a separate peace at the first opportunity. Meanwhile, the Italian colonies will attempt to negotiate with the British rather than wait for German overlords who will never reach their territory.
4. Between the flipping of Vichy France and the Italian colonies, the Mediterranean is secured quickly by the British Navy. If any German forces have made it across the sea, they are cut off and quickly forced to surrender.
5. The USSR continues to rearm after the Great Purge. When they enter the war, they will be far stronger than OTL.
6. The Nazi ideologues wonder why on earth the Fuhrer has given up on the entire overarching policy goal of the party. The military staff get nervous as they realise they have forsaken serious military advantages in the name of annexing colonies the Germans are never in any position to supply, let alone get troops or settlers or even a nominal government to in the first place.
The Allies begin planning landings on the continent years ahead of schedule, probably in Spain or Italy to take advantage of friendly populations in areas that Germany cannot easily supply.
Years later, and with a great deal of irony, it is accepted wisdom that not invading the USSR was the great strategic mistake of the short-lived Nazi regime.