Szydło said Macron’s task following his triumph on Sunday would be “undoubtedly difficult.”
“Europe is at a turning point - we have to face internal challenges related to Brexit and comprehensive reform of the EU, and external ones, dominated by security issues and the migration crisis,” wrote Szydło.
She added it was important for allies to speak with one voice and work together to ensure lasting peace and prosperity.
"Polish-French cooperation and the Weimar Triangle should play an important role in this process," said Szydło, referring to the Weimar group comprising Poland, Germany and France.
"In this context, I hope that your presidency will bring a new opening in our bilateral relations, at the political, economic and investment levels," she said.
Invitation to talks
She invited Macron to take part in Polish-French intergovernmental consultations.
Macron recently angered top officials in Warsaw when he suggested during his election campaign that Jarosław Kaczyński, the head of Poland's ruling party, is a “friend and ally” of Marine Le Pen, Macron's right-wing rival in the race for the French presidency, placing Kaczyński alongside Hungarian Prime Minister Viktor Orban and Russian President Vladimir Putin.
Meanwhile, a French daily cited Macron as suggesting that he wanted sanctions against Poland, which he said had “violated all the EU's principles”.
While speaking to striking factory workers of multinational white goods manufacturer Whirlpool, which will move some of its production to Poland, Macron accused Poland of playing on differences in labour costs.
Poland’s Foreign Minister Witold Waszczykowski then responded that "unjustified" accusations by Macron against Warsaw stemmed from France’s inability to compete with ever-stronger economies to the east.
In an interview with Poland’s Do Rzeczy weekly conducted before Macron’s win, Szydło said Warsaw would cooperate with the new French president, but added that "a politician who is bidding for important functions should weigh [his] words more.”
According to French authorities quoted by the Polish PAP news agency, with 99.99 percent of the vote counted, Macron had obtained the support of 66.06 percent of French voters.