alternatehistory.com

So what if there was no Vichy France . This is a difficult one as it was to Hitlers advantage to have a French rump state.
, President Albert Lebrun appointed the 84-year-old Pétain as his replacement on 16 June 1940. The Armistice with France (Second Compiègne) agreement was signed on 22 June 1940. A separate French agreement was reached with Italy, which had entered the war against France on 10 June, well after the outcome of the battle was decided.

Adolf Hitler had a number of reasons for agreeing to an armistice. He wanted to ensure that France did not continue to fight from North Africa, and he wanted to ensure that the French Navy was taken out of the war. In addition, leaving a French government in place would relieve Germany of the considerable burden of administering French territory, particularly as Hitler turned his attentions toward Britain. Finally, as Germany lacked a navy sufficient to occupy France's overseas territories, Hitler's only practical recourse to deny the British use of those territories was to maintain France's status as a de jure independent and neutral nation. However, Nazi espionage against France after its defeat intensified greatly, particularly in southern France.[11]


Maybe if you remove Petain from the mix due to death or ill health . Anyway some change that makes Hitler pursue the war with France longer without an armistice.

Hitler would need to expend more forces and face an active French navy and what ever other parts of the French armed forces that could be salvaged.
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