* President's party wins strong parliamentary majority
* French/German yield gap tightens towards 7-month lows
* Focus turns to Macron's reform agenda
* Brexit talks get under way in Brussels
* Euro zone periphery govt bond yields http://tmsnrt.rs/2ii2Bqr (Updates prices, adds comment)
LONDON, June 19 (Reuters) - The gap between French and German bond yields held near its tightest level in seven months on Monday, after French President Emmanuel Macron won a commanding majority in parliamentary elections, securing a strong mandate for pro-business reforms.
France's 10-year government bond yield was steady, also within sight of seven-month lows around 0.58 percent hit last week after a first round of parliamentary elections had pointed to a strong showing for Macron's party.
His centrist Republic on the Move LREM party and its centre-right Modem ally won 350 out of 577 seats in the lower house in Sunday's second-round vote, fewer than previously forecast.
Record low voter turnout suggested France's new leader, the youngest since Napoleon, would need to proceed cautiously with reforms in a country where trade unions and street protests have in the past forced new legislation to be diluted.
"He will also face an enormous amount of resistance on the ground from the vested interests of the trade unions which still wield an enormous amount of influence, and could make life very difficult for the inexperienced new President and his party," said Michael Hewson, chief market analyst at CMC Markets UK.
But the scale of his victory gives Macron, a pro-European Union centrist, a solid platform to carry out his campaign promises to revive the euro zone's second biggest economy.
That lifted investor sentiment on Monday, with French stocks rallying 1 percent and outperforming European peers. Banking stocks, a barometer of appetite for French assets, jumped over 1 percent .
Berenberg chief economist Holger Schmieding said France could become the strongest economy in Europe in a decade.
IN THE PAST
Sunday's vote also closes a chapter on what has been a driver of European market risk, given the popularity of anti-euro far-right leader Marine Le Pen heading into France's presidential elections in April and May.
The gap between French and German bond yields - an important gauge of risk appetite - had widened sharply heading into that vote but has since tightened.
The 10-year bond yield gap was at 35 bps on Monday, just 2 bps away from levels hit last week that marked the tightest since November. The spread is down more than 40 bps from highs hit in February at the height of French election jitters .
"What is also important is the composition of the (parliament)," said Peter Chatwell, head of euro rates strategy at Mizuho.
"Having the Socialists loose so many seats means this is still a very much business- and reform-friendly assembly and that's why we've been able to see the CAC-40 (stock market) rally nicely ...while French spreads are still relatively tight."
Positive developments in French politics contrasted with turbulence in Britain, where a weakened government on Monday kicked off divorce talks with the EU.
Outside France, most euro zone bond yields were a touch higher on the day.
For Reuters Live Markets blog on European and UK stock markets see reuters://realtime/verb=Open/url=http://emea1.apps.cp.extranet.thomsonreuters.bi z / c m s / ? p a g e I d = l i v e m a r k e t s
(Reporting by Dhara Ranasinghe, editing by Louise Heavens and John Stonestreet)