Researchers are underpaid and research is underfunded everywhere. Like most jobs that people find inherently interesting.
I don't know about the specific situation in France. In general, Europe spends more on academic research than the US, both in absolute terms and as a fraction of GDP. However, it's easier to make an academic career in the US. Because the gap between academic and industry salaries is wider in the US, Americans are more likely to leave the academia after PhD. And because employment-based immigration is particularly difficult in the US, many would-be immigrants end up doing a PhD without any intention of staying in the academia. Which means you have less competition if you stay in the academia in the US.
I don't know about the specific situation in France. In general, Europe spends more on academic research than the US, both in absolute terms and as a fraction of GDP. However, it's easier to make an academic career in the US. Because the gap between academic and industry salaries is wider in the US, Americans are more likely to leave the academia after PhD. And because employment-based immigration is particularly difficult in the US, many would-be immigrants end up doing a PhD without any intention of staying in the academia. Which means you have less competition if you stay in the academia in the US.