Hi Thierry,
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FIRST, & MOST IMPORTANT!
Silicon Dust make versions of their hardware for the US and European markets.
The Flex 4K seems to be for the US market only, so that WILL NOT WORK OVER HERE.
European models have -2DT or -4DT in their model name.
The Yankee ones have -US, and/or mention ATSC, which is their transmission standard.
See <https://info.hdhomerun.com/info/> and click on Connect or Flex under Hardware Info on that page.
Note also that the HDHomeRun is designed for "Free to Air" channels only -- not encrypted channels.
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I'm in the UK, so can only speak for TV over here; judging from reviews of the HDHomeRun on Amazon.fr, it seems to work over there, but "Your Mileage May Vary".
Short answer is ... it works fine. I have exactly the same setup as you plan.
The TV Picture looks very good on a 27" iMac -- I don't use my TV any more to watch.
In detail:
My iMac (2020, Intel, 27", with MacOS Sonoma) runs EyeTV 4 and connects via WiFi to my local network. The HDHomeRun is connected via Ethernet to the WiFi Access Point.
When you run EyeTV's Setup Assistant (for "geniatech" hdhomerun devices) the first time it scans for HDHomeRun tuners on the network, and from then onwards EyeTV detects the HDHomeRun, and just uses it.
I have a 5th Generation HDHomeRun Connect Quatro with 4 tuners (HDHR5-4DT).
It receives "standard" & HD channels (using DTT/T or DTT/T2, as needed).
The Quatro in the model name means it has 4 tuners, and Duo would mean it had 2 tuners.
EyeTV can only handle 2 of the tuners, ignoring the other two. However, it does work,
showing live TV (with pause/resume and recording) and does download and show the Over The Air programme guide.
It appears that the only difference between the Connect and Flex versions is that the Flex version has a USB socket to connect an external Disc.
Unless you will use Silicon Dust's own HDHomeRun app [and pay the £35! or whatever per year for that feature & off-air TV listings], there seems no way to use any external Disc connected to the HDHR Flex.
It isn't used (or needed) when using EyeTV, as that uses the Mac to store recordings.
=> the Flex models are effectively the same as the Connect models, and as EyeTV ignores any more than two tuners, the Duo or Quatro versions behave the same.
Alternatives:
In terms of hardware, Silicon Dust are the only modern network TV tuners I've seen that work with Macs. The old Netstream only supports DTT/T so it's outdated (and won't pick up HD broadcast channels; I know this as I had one :).
As you can see from the other forum topics, EyeTV 4 is buggy, but there aren't good alternatives for recording TV with a Mac, and at least over in the UK, it picks up the OTA programme guide and displays that well.
If you just want to watch live TV (with no pause/resume, no OTA programme guide display, and no recording), the HDHR works with VLC as well -- the HDHR runs a web server, and you can download a channel list (as a .m3u file from <http://hdhomerun.local/lineup.m3u>), add that to VLC, and just click on the channel list in VLC. Not having pause/resume for live TV (or recording) is a major limitation, but at least VLC doesn't crash.
Silicon Dust DO provide their own HDHomeRun app, but activating the recording function costs a non-trivial subscription charge per year. It's not clear if this software reads and displays the OTA programme guide -- they charge a subscription for their programme guide, so I suspect not.
I have not tried that software (as I think they're joking with their subscription prices) so cannot comment further.
all the best
Lawrence
p.s.: The HDHomeRun tuner also works perfectly with EyeTV 3 software, so if you have an old iMac, that works fine (without the added crashes of EyeTV 4).