Some 21 million people in 16 areas of France, including the capital Paris, are affected as the country fears a third wave.
In Poland, non-essential shops, hotels, cultural and sporting facilities are now closed for three weeks.
The country has the highest new daily rates of Covid cases since November.
Coronavirus cases are also rising exponentially in Germany, with Chancellor Angela Merkel warning it is likely that the country will now need to apply an “emergency brake” and re-impose lockdown measures.
The vaccine rollout across the European Union has been hindered by delayed deliveries, as well as the suspension in several countries of the use of the Oxford-AstraZeneca Covid-19 vaccine, over fears of possible side effects.
In France, the partial lockdown took effect from midnight on Friday.
Trains leaving Paris for parts of the country where lockdown restrictions do not apply, such as Brittany and Lyon, were reportedly fully booked hours before the measures were due to come into effect.
Traffic jams were reported on several roads leaving the capital.
The new restrictions are not be as strict as the previous lockdown, with people allowed to exercise outdoors.
Non-essential businesses are shut, but schools remain open, along with hairdressers if they follow a “particular sanitary protocol”.
France has reported more than 4.2 million infections since the start of the outbreak, with nearly 92,000 Covid-related deaths, according to the data compiled by Johns Hopkins University in the US.
In Poland, the three-week lockdown began on Saturday.
Polish health officials earlier warned the nationwide restrictions were necessary because of a rampant British variant of Covid-19 in the country. The variant now makes up more than 60% of infections.
Poland has had more than two million confirmed infections, and nearly 49,000 deaths, according to Johns Hopkins University.
Germany said on Friday it was now classifying neighbouring Poland as high risk. This means that from Sunday anyone crossing the border from Poland must provide a negative coronavirus test.
Source: News Agencies