I've done something roughly like this before on a VHF communications radio. It had a bunch of pre-programmed frequencies in its channel memory, but booted up to the "last used" channel when the power was turned on. Channel selection in the radio was using UP and DOWN buttons, not a selector switch. The user wanted a pre-selectable boot channel that was guaranteed to always be the first channel automatically provided.
What I did was to add a simple logic circuit that provided a sequence of operations on power-up. First it would sense power-up, then it would reset the radio to its "out of box" condition (which guaranteed that we started on channel 1), then electrically grab the UP and DOWN buttons and put a number of pulses on either UP or DOWN to suit the selection made on a switch that was included in the new circuit. This would force the radio up or down a certain number of times from channel 1 and then the logic circuit would release and do nothing until the next power cycle. In this way, you always booted to, say, CHAN 22, not to whatever was in use when the radio was turned off.
Adapting the general idea to your problem is not exactly obvious. It first depends on what your receiver does when the power is turned on. What frequency does it boot up to or start with? Does it first auto-scan the spectrum and remember which frequencies have signals on them? If you can figure out what the receiver does when the power is turned on, then perhaps a simple logic circuit could be added that replaces the Seek buttons entirely and that forces operation on a pre-selected channel.
One other idea is to insure that the receiver only receives your two FM signals and no others. If this were possible, then the seek buttons would only ever select one or the other, which may not get the users into any trouble. This idea is not easy to implement, and may be a non-starter. It would require that each receiver be shielded from the general spectrum somehow, which is quite difficult to do and then your signals would be piped into them in some way. Perhaps if you left the antenna off of your circuit board, and insured that your two desired signals were very strong, then perhaps the receiver would only hear those two. I'm skeptical that it could work that simply and reliably. It is more likely that other FM stations would be easily received even without an antenna connected, and therefore interfere with the operation.
Here is another idea that might work. If you added a CTCSS tone to your transmitter audio, which is not too difficult, you could then add a CTCSS decoder circuit to each receiver and this decoder would logically only allow the receiver to stop its seeking function on a frequency that carried this CTCSS tone. This would cause the receiver to only seek to your signals, not anyone elses. I can imagine the logical connection from CTCSS decoder circuit to the receiver circuit would also remove the SEEK buttons and replace them with a simple logic interface. It would be trivial to include a switch on each receiver allowing you to select whether it heard English or French by selecting the appropriate CTCSS tone. Encoders and Decoders were available in single chip form. You can build an encoder using a 567 chip, (it may suffer from inadequate stability, but there are many other ways to generate a fixed frequency using crystal control if that happens). Decoder chips used to be widely available many years ago, some from CML, but nowadays this function is often integrated with many other functions in radio controller ICs, so harder to find as a simple IC. Ramsey used to have a CTCSS kit, and it might still be available. A clever designer would be able to implement a decoder using a single PIC chip. Sourcing the decoder not withstanding (and many on this forum could help with this) I like this CTCSS idea the best. I expect it shouldn't cost any more than about $10 per receiver plus another $10 for the transmitter.
I am happy to assist further, even so far as to try designing something for you, but it would seem to make more sense to source a different FM receiver kit, one with fixed channels.