It appears that both of these claims are true. As reported by the AP, "French police said Friday they're investigating multiple cuts to fiber-optic cables in France's second-largest city. Operators said the cables link Marseille to other cities in France and Europe and that internet and phone services were severely disrupted." This is further corroborated by updates from Zscaler, a cloud security company, which stated, "We are aware of a major cable cut in the South of France that has impacted major cables with connectivity to Asia, Europe, the US, and potentially other parts of the world. As a result of the cable cut, customers may see packet loss and/or latency for websites and applications which traverse these impacted paths."
Released documents from the Scottish government confirm there was "damage to the primary telecommunications cable between the Scottish mainland and Shetland (via Orkney) which caused a telecommunications outage on Thursday 20th October 2022."
It's notable that the two events don't appear to be related. As reported by the same AP article cited above, "The damage in the city in southern France...appeared to resemble suspected acts of sabotage to other cables in the country earlier this year," whereas correspondence within the Scottish government incident (cited above) said "[Redacted] confirmed on 21 October 2022 that a fishing vessel was the cause of the outage." Further, the Guardian reported that the cable was severed "due to accidental damage to the cable by a UK-registered trawler," according to UK government officials.