Victory there would boost Johnson, and heap pressure on Starmer, as he tries to reposition the party after the hard-left leadership of his predecessor Jeremy Corbyn.
After rising above $1.42 in February to its highest level against the dollar since April 2018, sterling lost some ground versus the greenback in March.
The tournament was postponed by a year to June due to the pandemic and there remain questions over UEFA's plan to host the event in 12 cities across the continent.
Speaking at a daily coronavirus briefing, Sturgeon said: "Nobody wants to lose the Euros and I don't think we should be in the position right now of thinking that is the case.
After losing the 2014 independence vote, SNP leader Sturgeon is spearheading the push for another referendum and hopes to rejoin the EU should she fulfil her dream.
Brexit, which has dominated politics on both sides of the Channel since 2016, became reality an hour before midnight, ending the UK's 48-year obligation to follow Brussels' rules.