The spacecraft used for the transfer is going to have to be believably massive and is actually going to have to go to Mars and come back. That's a big chunk of a real manned Mars mission right there. People can see the thing in orbit and will be able to track it (particularly its engines when thrusting). The exhaust from the engines will also be a dead giveaway for it being significantly smaller than it is supposed to be. It will also be obvious if the rockets launching the components are smaller than they should be.
Even saving on things like life support and safety systems would be difficult. You are going to have to design and test the systems to maintain the illusion, otherwise the people doing that design will be suspicious. Or you could bring everyone involved in the design, testing, and construction into the conspiracy and hope that none of them leak anything, and then keep the designs secret so outsiders can't check them, otherwise the fact that no effort was made in designing them would become obvious.
You are going to have to have a fake crew. Their training is going to be fairly visible, and so will cost about as much for a fake mission as a real one. They are also going to have to go into hiding for the duration of the mission proper (months to years). To be believable they are also going to have to be the kind of people who would be expected to go on such a mission. Reasonably well known members of the scientific community and possibly from military aviation (the latter probably being less likely for the ESA than for NASA) using a "no name" crew is going to be suspicious, as will an all military crew from the ESA.
So you have to get a group of scientists, respected ones who will have a strong interest in having a real manned mission to Mars to agree to go through all the difficult training, and then go into hiding for over a year, then keep the secret for decades afterwards. This would be a massive breach of scientific ethics and a commensurate risk to the professional reputations that's essentially certain to be uncovered eventually, even if the hoax could be pulled off temporarily.
The crew are also going to expected to interact with Earth on video (with appropriate time delay) while in transit. So fake zero-G footage will need to be prepared on time scales ranging from immediately to half an hour as the mission progresses. Free fall in an aircraft can't be faked for long enough and the other option is "hiding" on a human habitable spacecraft in orbit. (which would need to be built in addition to the fake Mars ship) and would require getting the crew to it rather than the Mars ship (secretly), then down to Earth to fake the landing without anyone noticing, then back up again without anyone noticing to fake the trip back, and then get them back down without anyone noticing that they came from the wrong spacecraft.
A spin gravity habitat could be included on the fake ship, but spin gravity, especially on a small enough diameter to be practical to build with current technology would have noticeable differences from real gravity. It would also make the fake ship more expensive to build, and viewers might wonder why the crew never send videos from the zero gravity area of the ship (at least not pre-recorded videos or ones with time for post production special effects, or short enough ones to be made from a diving aircraft.
In short, it's even more laughable than the idea of the moon landings being fake, even if you go through the complete motions of sending a crew capable ship and just not putting any people on it, which would be just as expensive and so would completely defeat the point, and built another long term human habitable spacecraft in orbit in secret.