The Party of the European Left, which sits in the United European Left - Nordic Green Left group in the European Parliament, is a left-wing Europarty that's running Greek opposition leader Alexis Tsipras as its candidate for the Commission Presidency. It's the second smallest party in the Parliament and is further to the left of the PES and the European Greens, but some of its member parties have gained strength nationally, such as SYRIZA in Greece. In its manifesto (PDF), the European Left sets itself up as the anti-austerity party and an opponent of the EU-US Trade Agreement.
As well as being anti-austerity, the European Left opposes privatisation in general and highlights its opposition to the privatisation of natural resources. It wants to regain power over the world of finance, protect the rights of workers and trade unions, and focus the Common Agricultural Policy to ensure food security. The European Left wants the EU to preserve its independence versus the US and NATO, demands the suspension of the Israel-EU Association Agreement for human rights reasons and pushes for the reform of the Union for the Mediterranean (which it accuses of helping destabilise the region) and the renegotiation of free trade agreements with Latin America and the Caribbean (to make them benefit the people more).
On the Eurozone, the European Left wants the abolition of a large part of public debt (freezing its repayment) and the ECB to be reformed so that it becomes the lender of last resort and offer loans directly to over-indebted Member States (which would require treaty change, I think). The European Left would abolish the Fiscal Pact and the "6-pack" of measures that regulate Eurozone budgets. Corporate taxation would be harmonised, and employment would be boosted by investment from the European Investment Bank and the European Left advocate the creation of a "European public bank of social and solidarity-based development" that would fund projects on the basis of social and environmental criteria. The European Left aims towards the public and democratic control of strategic sectors of the economy and towards a 35 hour working week.
In agriculture, the European Left would tax imports and exports that destablise the local market in order to finance the relocalisation of production, stop support for biofuels and regulate the margins and practices of agrifood giants and retailers. The European Left would have a similar relocalisation focus for industry.
The European Left is against the membership of NATO (of the Member States and wants immediate withdrawal from the alliance. They also oppose the militarisation of the EU.
The Party of the European Left is running n a hard-left platform. Not only is it anti-austerity, but its focus on "relocalisation" of agriculture and industry seems to be a policy of de-globalisation and autarky. If you are strongly anti-globalisation and favour turning from international free trade agreements to relocalisation, then the Party of the European Left might be for you.