As a dual national, you will also need to file U.S. tax returns (as a resident) for the rest of your life – but be careful because if you take the exclusion of income earned abroad in the U.S. United States (to exclude your wage income from US tax), then you cannot deduct your 401K contributions from gross income for US tax purposes, so you will end up paying both US and French tax on your wage income (there is the foreign tax credit which you can use to offset taxes on wages paid in France against your US tax bill – but this can quickly get complicated).
You should probably speak to a tax advisor in the United States before you go. It may be possible to convert your solo/personal 401K to an IRA account – although you can’t make any more contributions once you’re resident abroad, it may be possible to just let it sit and collect income until you reach retirement age and can start receiving distributions. Account income (401K or IRA) is not taxed by the French – and after you retire, you will pay US tax on your withdrawals and receive a full credit at French rates on your French income taxes (without ” contributions” deducted from the amount of the pension).