In France, there are always enough polling stations. Schools and town halls are polling stations. More people whose ballots to count? That's automatically more people to run polling stations and count the votes. The very notion that some areas may be disenfranchised by lack of polling stations is inconceivable.
In France, people must show ID to vote, and must register in advance where they will vote with their ID, so multiple-vote fraud is almost impossible: it would require complicity between multiple government services, that check the one-to-one-to-one correspondence between people and identity documents and polling stations. Even then, a cheat there would leave quite a paper trail, especially as polling stations record who voted. For that effort, each cheater with duplicate identities could only go to so many different polling stations in a day. Massive fraud would be hard to pull off, and even harder to conceal.
In France, there are no complex ballots on which one needs to do markings with the right kind of pen. No confusion as to how to mark ballots. No manipulation by making some names come first or appear multiple times. No subjective judgment to declare which ballots are valid and how interpret them. No need for expensive untrustworthy machines to process them in a timely fashion. Instead, voters are sent one clearly printed ballot for each of the available options. The same ballots are also available at the polling station. Each voter goes in an isolation booth, puts his ballot of choice in an envelope, then gets out of the booth and publicly puts the single envelope in the ballot box after his ID is verified and name is checked off by assessors of multiple rival parties. When the boxes are counted, in public, only envelopes containing a single unadulterated unmarked untorn uncrumpled pristine genuine ballot are counted as valid. The process and the criteria it applies are fairly clear, objective, hard to get wrong, and hard to dispute.
In France, ballots are cast in transparent ballot boxes in front of everyone. The boxes stay in full view of everyone until they are emptied and the ballots counted the same day at the same site by many people of all parties. The counts are reported immediately by phone in presence of the assessors, who also sign the report, that can be checked thereafter for each polling station. There is no opportunity for anyone to stuff ballot boxes or insert fake numbers in the counting. There is no counting by "machines" that can be pre-programmed or hacked to cheat. There is no keeping ballot boxes overnight where they can be tampered with. There is no set of privileged people with access to ballot boxes who can do a switcheroo or a stuffaroo.
In France, there are no "mail in ballots", where anyone with suitable access could insert or delete thousands of ballots with no way to assess afterwards the integrity of the process. If for some reason you cannot be present on the ballot day, you can register in advance to give your voting proxy to someone you trust to vote for you. But no one may be delegated more than two proxies, thus closing an obvious venue for massive fraud.
In France, it's the people themselves, not the communist "civil service", that runs the elections with every step along the way checked by many people from many rival parties. The only exception is the one-to-one-to-one correspondence between voters, IDs and polling places, but that's not massively gamable without detection. Therefore, the count of the ballots is widely considered trustworthy by everyone and never contested, while requiring no advanced technology whatsoever beyond opaque envelopes and transparent ballot boxes. French people watch with deep contempt and appallment the baroque, expensive, unfair, seemingly absurd, and completely untrustworthy process used in the USA.
AND YET, in France, the communists still cheat and still conquered Power, in an irreversible tight grip. It's just that they don't do it by tampering with the count. They do it by completely controlling the schools, the mass media, the campaign finances, the "civil service", and the courts. Thus, they can brainwash people, spread their uncontradicted narrative, defund any opposition, harass any opponent out of being able to afford a living, and fine or imprison the occasional overly active opponent. If people vote "wrong", they will just force a re-vote until they vote "right" at which point the change will be made irreversible (as for the European Constitution).
In the USA, the communists control schools and media, but not so completely that they can totally hush opposing ideas: churches, a few exceptions like FOX, and now the Internet, break their stranglehold. Communists control the Democratic Party, the "civil service" in all cities and at the federal level, but don't control (all) the courts, so can't arbitrarily oppress their opponents. They control public funding, but there is just too much private funding that they cannot control, so they can't just defund their opponents. That is why they resort to tampering with ballots using a system OBVIOUSLY DESIGNED to enable fraud.
What's even more "funny" is that both voter registration and mail-in votes make a mockery of ballot anonymity—and then in modern times, preferences are obvious on social media and via the massive government surveillance. Since anonymity doesn't meaningfully exist, a trivially simple and obviously cheat-proof process would just be to make all votes public and count them, then leave enough time for losers to triple check that it was all legit. So, really, the complexity of the process is not even justified by anonymity as it is in France. (Whether anonymity is itself a good thing or not is another question.)
In the end, you have no way to trust the process. Not only that, it is obvious that SOONER OR LATER the process is bound to be exploited. You can be naive and believe it wasn't exploited YET (but then, you better provide an explanation compatible with the existence of gerrymandering). However you are stupid, evil or crazy (alternatives not exclusive) if you believe it's a trustworthy process the results of which you and everyone else should blindly accept as the basis for Political Sovereignty.
Elections are a sham. Always have been. Always will be. Like France's only serious and honest presidential candidate, ever, said: "If voting could change anything, it would have been prohibited long ago." (« Si voter changeait quelque chose, il y a longtemps que ça serait interdit. » — Coluche)