If the French person will be taxed in France based on French revenu a good option is usually the Plan Epargne Action (PEA) on an online broker (Bourse Direct, BforBank, boursorama…). The transaction cost are usually minimal 1,9-2,5% for French and European shares or ETF (mostly synthetic or swapped). Look for a provider that wonn’t charged custody fees.
The broker will provide an Imprimé Fiscal Unique (IFU) every year for the tax declaration anf it will be prefilled with the information exchanged with the French Tax department.
The benefits will be to be taxed on dividend or capital gain only at withdraws after 5 years.
As suggested before an online Life Insurance broker (like MesPlacements, Linxea …) will be more suited for someone of 60 y.o. with no risk tolerance. They charged 0,50-0,70% management fee and will offer low risk/low gain French bonds named Fond Euro or REIT or SCPI or fraction shares. The main benefit remains a no taxation account until withdraws and in a strategy of optimising succession taxes.