* German Q2, 2023, Q3, 2023 and French Q3, 2023 at records

* Weather, gas and French nuclear factors cited

* Hot weather curbs cooling water, hampers barge loads

FRANKFURT, Aug 8 (Reuters) - Some 2023 German and French quarterly electricity contracts set record highs on Monday on the European wholesale market, driven by concerns about Russian gas supply and hot and dry weather, which have already lifted spot prices.

Traders said the market was nervous because the prompt outlook is underpinned by expectations of continued drought, while prices further along were responding to a mix of gas scarcity and reactor problems in nuclear-reliant France, which is interconnected with Germany.

France's regulator extended temporary waivers allowing five power stations to continue discharging hot water into rivers as the country contends with a fourth heatwave of the summer, which worsens already low capacity levels.

The weather has also curbed river levels, hampering the transport of coal to power plants as barges cannot sail fully-laden.

At 1330 GMT, German baseload supply for second-quarter 2023 was up 4.1% at 374.8 euros ($382.07) a megawatt hour (MWh) and third-quarter 2023 was up 3.3% at 374.1 euros , while French second-quarter 2023 was up 7.5% at 349.5 euros.

"Gas and weather are set to remain important factors for European energy prices," said Andy Sommer, team leader fundamental analysis & modelling at Swiss utility Axpo, in a market note.

Sommer referred to curbs on the Nord Stream 1 gas pipeline and weather forecasts indicating longer above-normal temperatures.

Power also interacted with firmer gas which is burnt for power in competition with coal.

Power has been surging in July and into August after Russian exporter Gazprom did not fully restart Nord Stream 1 after maintenance, citing trouble with a turbine.

This has further tightened scarce gas supply and resulted in frantic moves to build up inventories in Europe, bail out financially squeezed importers in Germany, and raise imports of liquefied natural gas (LNG).

In addition, German policymakers are trying to reserve gas for direct use by manufacturers rather than for electricity to protect the performance of the country's export-oriented industry, intensifying the scramble for supply.

($1 = 0.9810 euros) (Reporting by Vera Eckert; Editing by David Holmes)